Preface

Chapter 8 **Testing Physical and Mathematical Criteria in a New Meandering Autocorrelation Function 205**

Chapter 9 **Underwater Optical Wireless Communication Systems: A**

Degrazia

**VI** Contents

**Concise Review 219**

George S. Tombras

Charles R.P. Szinvelski, Lidiane Buligon, Michel Baptistella

Stefanello, Silvana Maldaner, Debora R. Roberti and Gervásio Annes

Lydia K. Gkoura, George D. Roumelas, Hector E. Nistazakis, Harilaos G. Sandalidis, Alexander Vavoulas, Andreas D. Tsigopoulos and

> Despite intense development of computational technologies, achievements in the area of construction of numerical methods and development of commercial and open-source soft‐ ware, improvements of experimental methods, and high-performance computing facilities, the problem of modelling and simulation of turbulence remains one of the most complex and important problems of fluid dynamics. In contrast to laminar flows whose computation has already become a routine procedure, reliable prediction of turbulent flows is more art than rigorous science for numerous reasons including three-dimensional nature of the flow, stochastic character, and a wide spectrum of spatial and temporal scales.

> A detailed knowledge of the flow regimes is of crucial interest for improving performance of many engineering devices including mixing chambers, turbine blade passages, and engines. Accurate prediction of turbulent flows remains a challenging task despite considerable work in this area and the acceptance of computational fluid dynamics (CFD) as a design tool. The application of computational techniques to the design and optimization of engineering devi‐ ces is difficult because of the complexity of flows subjected to, among others, phenomena, confinement, boundary layers, rotation effects, Ekman layers on rotating surfaces, stagna‐ tion flow heat transfer, heat transfer in the presence of steep pressure gradients both favour‐ able and adverse, free stream turbulence, and three-dimensional effects such as tip leakage flow and secondary flows.

> The quality of CFD calculations of the turbulent flows and heat transfer in boundary layers, free mixing layers, and free and impinging jets strongly depends on the proper prediction of turbulence phenomena. Investigations of heat transfer, skin friction, flow separation, and reattachment effects demand a reliable simulation of the turbulence, reliable numerical methods, accurate programming, and robust working practices. A necessary step consists in the verification and validation of numerical algorithms and turbulence models for idealized geometries, which can be performed only if experimental data are available for compari‐ sons.

> CFD provides three main options to turbulence simulation, including direct numerical simu‐ lation (DNS), large-eddy simulation (LES), and solution of Reynolds-averaged Navier-Stokes (RANS) equations.

> DNS implies solving the full (unsteady and three-dimensional) Navier-Stokes equations, which allows obtaining instantaneous characteristics and resolving all scales of a turbulent flow, if numerical and other types of errors can be avoided. The resultant statistics is used to validate turbulence models, to develop methods of flow control, and to study the laminarturbulent transition. As the capabilities of measurement equipment are limited, DNS is con‐

sidered as an additional source of experimental data, e.g., pressure fluctuations, vorticity, and dissipation rate of the turbulent kinetic energy. Limitations in the use of DNS are high requirements to finite difference schemes, satisfaction of initial and boundary conditions, and limited computational resources. Time and mesh steps are of the order of Kolmogorov's scales of time and length and decrease with increasing Reynolds number. Obtaining a statis‐ tically steady flow pattern requires tens and hundreds of hours of processor time. The use of unstructured meshes also contributes to consumption of computer memory and processor time. It is difficult to implement computations that involve DNS except for low Reynolds numbers and simple flow geometry.

Solution of RANS equations requires much lower computational resources and is success‐ fully used in engineering practice. The issues of closure are solved at different levels of com‐ plexity. Turbulence models are classified in terms of the number of equations introduced in addition to the RANS equations. An increase in the number of equations requires additional semi-empirical information to be involved, which spoils model universality. Available tur‐ bulence models do not possess acceptable universality and, therefore, cannot be used to solve a wide range of applied engineering problems.

The lack of a universal turbulence model suitable for computing all or at least most turbu‐ lent flows shifted the focus in turbulence research. Improved capabilities of CFD tools and high-performance resources stimulated the search for and application of approaches that are more rigorous and universal than RANS.

LES is a compromise between DNS and solution of RANS equations. LES implies solution of filtered Navier-Stokes equations. Large eddies, being under a direct action of boundary con‐ ditions and carrying the maximum Reynolds stresses, are computed. Small eddies have a more universal structure and are modelled by sub-grid scale (SGS) models based on the ed‐ dy viscosity or other rational approximations of transport processes. SGS models are nor‐ mally characterized by significant diffusion and dissipation, which allows one to overcome computational problems caused by presentation of small eddies on a chosen mesh and to stabilize numerical computations. As LES excludes direct computations of small eddies, the time and mesh steps are much greater (approximately by an order of magnitude) than Kol‐ mogorov's scales of length and time. Higher Reynolds number than that in the DNS can be achieved with a fixed computational memory.

A large number of SGS models, filters, boundary conditions, and finite-difference schemes have been tested in numerous computations. Nevertheless, neither the optimal choice of the SGS model is clear nor the choice, if made, is justified. There are no universal near-wall functions providing a decrease in the number of nodes in the near-wall region; therefore it is difficult to use LES for computing flows with small separation regions and transition points. Yet, LES is a promising direction in the development of methods for computing turbulent flows and seems to be a serious alternative to DNS and RANS.

There are also hybrid approaches that combine some features of DNS, RANS, and LES, in particular, Detached Eddy Simulation (DES) and hybrid RANS-LES approaches. The main motivation for hybridizing the two methods is to decrease the cost of the traditional LES method, which is large because of the requirement to directly capture all the scales of mo‐ tion responsible for turbulence production and the observed inability of most SGS models to correctly account for anisotropy and non-equilibrium nature of the flows.

DES is a modification of a RANS model in which the model switches to SGS formulation in regions fine enough forLEScalculations. Regions near solidboundaries and where the turbu‐ lent length scale is less than the maximum mesh dimension are assigned the RANSmode of solution. As the turbulent length scale exceeds the mesh dimension, the regions are solved using the LES mode. Therefore, the mesh resolution is not as demanding as pure LES, there‐ by considerably cutting down the cost of thecomputation.

The book gives an overview of various approaches to turbulence simulation and highlights possible weaknesses in the CFD codes and suggests some possible improvement paths. The current scientific status of simulation of turbulent flows as well as some advances in compu‐ tational techniques and practical applications of turbulence research is reviewed and consid‐ ered in the book. The book also covers issues related to development, verification, and validation of turbulence models and focuses on development of the best practice for engi‐ neering calculations.

## **Critical assessment of hybrid RANS-LES modelling for attached and separated flows**

The dynamic hybrid RANS and LES modelling framework is assessed in the chapter. Com‐ putations of two benchmark test problems, turbulent channel flow and backward-facing step flow, are performed to assess the model for attached and separated turbulent flows. This investigation attempts to evaluate the ability of the hybrid method to reproduce the detailed physics of attached and separated turbulent flows as well as to resolve the delayed break down of separated shear layers. The computed results are compared with experimen‐ tal and computational data based on RANS and DNS. The comparison demonstrates that the model addresses many of the weaknesses inherent in common models.

## **Numerical analysis of laminar-turbulent bifurcation scenarios in Kelvin-Helmholtz and Rayleigh-Taylor instabilities for compressible flow**

The laminar-turbulent transition in compressible flows triggered by Kelvin-Helmholtz and Rayleigh-Taylor instabilities is considered in the chapter. Floquet theory is applied to the linearized problem using matrix-free implicitly restarted Arnoldi method. The numerical calculations are performed for some benchmark test problems, and laminar-turbulent devel‐ opment of compressible Kelvin-Helmholtz and Rayleigh-Taylor instabilities as the bifurca‐ tion scenarios is shown.

#### **Interface instability and turbulent mixing**

sidered as an additional source of experimental data, e.g., pressure fluctuations, vorticity, and dissipation rate of the turbulent kinetic energy. Limitations in the use of DNS are high requirements to finite difference schemes, satisfaction of initial and boundary conditions, and limited computational resources. Time and mesh steps are of the order of Kolmogorov's scales of time and length and decrease with increasing Reynolds number. Obtaining a statis‐ tically steady flow pattern requires tens and hundreds of hours of processor time. The use of unstructured meshes also contributes to consumption of computer memory and processor time. It is difficult to implement computations that involve DNS except for low Reynolds

Solution of RANS equations requires much lower computational resources and is success‐ fully used in engineering practice. The issues of closure are solved at different levels of com‐ plexity. Turbulence models are classified in terms of the number of equations introduced in addition to the RANS equations. An increase in the number of equations requires additional semi-empirical information to be involved, which spoils model universality. Available tur‐ bulence models do not possess acceptable universality and, therefore, cannot be used to

The lack of a universal turbulence model suitable for computing all or at least most turbu‐ lent flows shifted the focus in turbulence research. Improved capabilities of CFD tools and high-performance resources stimulated the search for and application of approaches that are

LES is a compromise between DNS and solution of RANS equations. LES implies solution of filtered Navier-Stokes equations. Large eddies, being under a direct action of boundary con‐ ditions and carrying the maximum Reynolds stresses, are computed. Small eddies have a more universal structure and are modelled by sub-grid scale (SGS) models based on the ed‐ dy viscosity or other rational approximations of transport processes. SGS models are nor‐ mally characterized by significant diffusion and dissipation, which allows one to overcome computational problems caused by presentation of small eddies on a chosen mesh and to stabilize numerical computations. As LES excludes direct computations of small eddies, the time and mesh steps are much greater (approximately by an order of magnitude) than Kol‐ mogorov's scales of length and time. Higher Reynolds number than that in the DNS can be

A large number of SGS models, filters, boundary conditions, and finite-difference schemes have been tested in numerous computations. Nevertheless, neither the optimal choice of the SGS model is clear nor the choice, if made, is justified. There are no universal near-wall functions providing a decrease in the number of nodes in the near-wall region; therefore it is difficult to use LES for computing flows with small separation regions and transition points. Yet, LES is a promising direction in the development of methods for computing turbulent

There are also hybrid approaches that combine some features of DNS, RANS, and LES, in particular, Detached Eddy Simulation (DES) and hybrid RANS-LES approaches. The main motivation for hybridizing the two methods is to decrease the cost of the traditional LES method, which is large because of the requirement to directly capture all the scales of mo‐ tion responsible for turbulence production and the observed inability of most SGS models to

numbers and simple flow geometry.

VIII Preface

solve a wide range of applied engineering problems.

more rigorous and universal than RANS.

achieved with a fixed computational memory.

flows and seems to be a serious alternative to DNS and RANS.

correctly account for anisotropy and non-equilibrium nature of the flows.

Numerical investigation of the Richtmyer-Meshkov instability and turbulent mixing is pre‐ sented in the chapter. The verification and validation of numerical method and computer code, the growth laws and mechanics of turbulent mixing, the effects of initial conditions, and the dynamic behaviour and some new phenomenon for Richtmyer-Meshkov instability and turbulent mixing are discussed.

#### **Statistical modelling for the energy-containing structure of turbulent flows**

The development of statistical theory for the energy-containing structure of turbulent flows, taking into account the phenomenon of internal intermittency, is proposed in the chapter. New differential equations for conditional means of turbulent and non-turbulent flow are established. A new principle of constructing mathematical models as the method of autono‐ mous statistical modelling of turbulent flows is presented. Testing of the method is accom‐ plished on the example of constructing a mathematical model for the conditional means of turbulent flow in a mixing layer.

## **Turbulence and its effects on aerodynamics of flow through turbine stages**

The turbulence features and their impact on fluid dynamics, streaming of blades, and effi‐ ciency performance are carried out in the chapter. The turbulence effects and transition on‐ set in turbine stages, approaches to their modelling, and how they affect efficiency and flow parameter distribution and lead to an innovative design are discussed.

## **Turbulence transport in rotor-stator and stator-rotor stages for axial flow fans**

Recent developments concerning numerical simulation of rotor-stator and stator-rotor inter‐ actions in low-speed axial fans using LES techniques are presented in the chapter. A postprocessing framework is introduced to segregate the deterministic and turbulent components of the unsteady flow, allowing an accurate description of both phenomena. The ability of LES computations to disclose flow turbulence in rotor-stator environments at offdesign conditions is demonstrated.

#### **RANS modelling of turbulence in combustors**

In this chapter, some widely used RAMS turbulence models are discussed and validated against a comprehensive experimental database from a model combustor. The results ob‐ tained show that the flow features are captured by all turbulence models. However, in terms of quantitatively predicting the velocity, temperature, and species fields, various degrees of agreement with the experimental data are observed. It is found that the turbulent Prandtl and Schmidt numbers have a significant effect on the predicted temperature fields in the combustor and the temperature profile.

#### **Testing physical and mathematical criteria in a new meandering autocorrelation function**

An alternative formulation for the low-wind speed meandering autocorrelation function is presented in the chapter. This expression for the meandering autocorrelation function repro‐ duces well-observed wind meandering data measured in a micrometeorological site located in a Pampa ecosystem area. The comparison shows that the alternative relation for the meander‐ ing autocorrelation function is suitable to provide meandering characteristic parameters.

#### **Underwater optical wireless communication systems: a concise review**

Underwater optical wireless communication (UOWC) has gained a considerable interest as an alternative means for broadband inexpensive submarine communications. It was demon‐ strated that UOWC networks are feasible to operate at high data rates for medium distances up to a hundred meters. However, it is not currently available as an industrial product, and mainly test-bed measurements in water test tanks have been reported so far. The chapter summarizes the recent advances in channel modelling and system analysis and design in the area of UOWC.

The book covers the current state, development prospects, and engineering applications of turbulence science representing the latest research of various groups of internationally rec‐ ognized experts. This book is intended for engineers and technical workers whose work is related to predictions of turbulent flow properties in science and engineering. It will be of interest to academics working in environmental engineering and to industrial practitioners in companies concerned with design and optimization of engineering systems.

The open exchange of scientific data, results, and ideas will hopefully lead to improved pre‐ dictions of turbulence impact on industrial and technological processes. The book presents necessary data and helpful suggestions to advance understanding of the turbulent phenom‐ ena.

plished on the example of constructing a mathematical model for the conditional means of

The turbulence features and their impact on fluid dynamics, streaming of blades, and effi‐ ciency performance are carried out in the chapter. The turbulence effects and transition on‐ set in turbine stages, approaches to their modelling, and how they affect efficiency and flow

Recent developments concerning numerical simulation of rotor-stator and stator-rotor inter‐ actions in low-speed axial fans using LES techniques are presented in the chapter. A postprocessing framework is introduced to segregate the deterministic and turbulent components of the unsteady flow, allowing an accurate description of both phenomena. The ability of LES computations to disclose flow turbulence in rotor-stator environments at off-

In this chapter, some widely used RAMS turbulence models are discussed and validated against a comprehensive experimental database from a model combustor. The results ob‐ tained show that the flow features are captured by all turbulence models. However, in terms of quantitatively predicting the velocity, temperature, and species fields, various degrees of agreement with the experimental data are observed. It is found that the turbulent Prandtl and Schmidt numbers have a significant effect on the predicted temperature fields in the

**Testing physical and mathematical criteria in a new meandering autocorrelation function** An alternative formulation for the low-wind speed meandering autocorrelation function is presented in the chapter. This expression for the meandering autocorrelation function repro‐ duces well-observed wind meandering data measured in a micrometeorological site located in a Pampa ecosystem area. The comparison shows that the alternative relation for the meander‐ ing autocorrelation function is suitable to provide meandering characteristic parameters.

Underwater optical wireless communication (UOWC) has gained a considerable interest as an alternative means for broadband inexpensive submarine communications. It was demon‐ strated that UOWC networks are feasible to operate at high data rates for medium distances up to a hundred meters. However, it is not currently available as an industrial product, and mainly test-bed measurements in water test tanks have been reported so far. The chapter summarizes the recent advances in channel modelling and system analysis and design in the

The book covers the current state, development prospects, and engineering applications of turbulence science representing the latest research of various groups of internationally rec‐ ognized experts. This book is intended for engineers and technical workers whose work is related to predictions of turbulent flow properties in science and engineering. It will be of interest to academics working in environmental engineering and to industrial practitioners

in companies concerned with design and optimization of engineering systems.

**Underwater optical wireless communication systems: a concise review**

**Turbulence and its effects on aerodynamics of flow through turbine stages**

**Turbulence transport in rotor-stator and stator-rotor stages for axial flow fans**

parameter distribution and lead to an innovative design are discussed.

turbulent flow in a mixing layer.

X Preface

design conditions is demonstrated.

combustor and the temperature profile.

area of UOWC.

**RANS modelling of turbulence in combustors**

## **Dr Konstantin Volkov, MEng, MSc, PhD, DSc, CEng, MIMechE, MInstP**

Department of Mechanical and Automotive Engineering School of Mechanical and Aerospace Engineering Faculty of Science, Engineering and Computing Kingston University London, United Kingdom
