Robert Prosser

Synthetic Inflow Boundary Conditions for Wall Bounded Flows

The present paper summarizes the research conducted at the University of Manchester over the course of the Desider project on methods of generation of synthetic turbulence. A random procedure, referred to as the Synthetic Eddy Method (SEM), based on the classical view of turbulence as a superposition of coherent structures was developed and compared with other methods of generation of inflow boundary conditions for LES, for different types of wall bounded flows. Synthetic inflow generation methods always show a transition region downstream of the inlet until the turbulence recovers an equilibrium state. The sensitivity of this transition region to variations in the synthetic inflow turbulence energy, length scale and time scale is studied herein with applications to hybrid RANS-LES methods in mind, as RANS results cannot be expected to provide accurate values for these scales to the LES region. A parameterization of the SEM suitable for hybrid RANS-LES simulations is proposed and tested on hybrid RANS-LES simulations of several wall bounded flows, with an emphasis on the flat plat boundary layer.

An adaptive algorithm for compressible reacting flows using interpolating wavelets

Abstract A new wavelet-based method for the simulation of reacting flows on adaptive meshes is presented. The method is based on the removal of grid points whose wavelet coefficients are small with reference to some user-specified threshold. Unlike some other collocation methods, the scheme simulates flow behaviour in the physical (i.e. not transformed) domain, and the wavelets, thus, provide the method by which the derivatives appearing in the transport equations are calculated. The wavelet transformis based on a subtraction algorithm, and circumvents the hanging node problem associated with other adaptive strategies. Interpolating wavelets are applied to a compressible one-dimensional laminar flame problem with time dependent boundary conditions. We find that the resolution of the chemistry distribution is comparatively straightforward. The same is not true of the pressure field, which demonstrates sensitivity to the imposed threshold level. Conclusions and directions for future work are presented based on these findings.

Development of an Alternative Delayed Detached-Eddy Simulation Formulation Based on Elliptic Relaxation

CD = drag coefficient CDDES = empirical parameter Cf = skin-friction coefficient CL = lift coefficient Cp = pressure coefficient Ce1 = model constant for the dissipation equation Ce2 = model constant for the dissipation equation c = chord length f = elliptic operator fd = delayed detached-eddy simulation blending function h = hill height k = turbulent kinetic energy L = turbulent length scale Re = Reynolds number S = deformation tensor Ub = bulk velocity U∞ = freestream velocity y = distance to the nearest wall y = nondimensional wall distance Δ = large-eddy simulation filter width Δt = time step e = turbulent dissipation κ = von Karman constant ν = molecular viscosity νt = turbulent viscosity Ψ = delayed detached-eddy simulation correction term

An evaluation of noise reduction algorithms for particle-based fluid simulations in multi-scale applications

Filtering of particle-based simulation data can lead to reduced computational costs and enable more efficient information transfer in multi-scale modelling. This paper compares the effectiveness of various signal processing methods to reduce numerical noise and capture the structures of nano-flow systems. In addition, a novel combination of these algorithms is introduced, showing the potential of hybrid strategies to improve further the de-noising performance for time-dependent measurements. The methods were tested on velocity and density fields, obtained from simulations performed with molecular dynamics and dissipative particle dynamics. Comparisons between the algorithms are given in terms of performance, quality of the results and sensitivity to the choice of input parameters. The results provide useful insights on strategies for the analysis of particle-based data and the reduction of computational costs in obtaining ensemble solutions.

Modelling Flame turbulence interaction in RANS simulation of premixed turbulent combustion

Flame turbulence interaction is an important term for modelling scalar dissipation in premixed turbulent combustion. In order to obtain an accurate representation of the flame turbulence interaction phenomenon, an evolution equation for has recently been proposed. This equation gives a detailed insight into the flame turbulence interaction phenomenon and provides an alternative approach to modelling the important physics represented by . In this paper the evolution equation is used to model a premixed propane–air flame stabilised in a turbulent mixing layer. The simulations are carried out in the context of a Reynolds Averaged Navier–Stokes (RANS) framework and the results are compared with the experiments and also with Large Eddy Simulation (LES). It is found that the modelling strategy involving the evolution equation gives good approximations for the mean velocities and flame locations in the mixing layer stabilised flame when compared with other modelling strategies.

Wavelet methods in computational combustion

Discretisation schemes based on the use of wavelet methods offer many potential advantages for the numerical simulation of combustion. In many cases of interest, flame structures are thin relative to the largest length scales of the problem and most length scales of the flow field, and so lend themselves to simulation using adaptive-mesh methods. Wavelet methods are naturally adaptive, in that the coefficients of the wavelet transform are non-zero only in regions where there is significant variation present in the solution. Hence, simple thresholding can be employed to make valuable savings in storage and in execution time. In this chapter, the basic principles of wavelet methods are established. Orthogonal and biorthogonal wavelet formulations are described and their advantages and disadvantages are discussed. An illustration of a wavelet-based discretisation scheme is provided using the Navier-Stokes momentum equation as an example. The same wavelet approach is applied to the simulation of a one-dimensional laminar premixed flame for which an asymptotic solution exists. Comparisons are made between the computational and analytical results and the accuracy of the wavelet approach is assessed. Extensions to higher dimensions are discussed. Finally, the current state of development of wavelet methods is outlined and conclusions are drawn.

On the effects of Lifting on Interpolating Wavelets for Combustion Simulations

Abstract The use of wavelets - and more generally multi-resolution analysis (MRA) - for the solution of non-linear partial differential equations (PDEs) is an active area of research, with many schemes currently available. Recently, a scheme has been developed, which employs biorthogonal interpolating wavelets, and which has been applied to problems in combustion [31]. Of central importance to this method is the discretization of the derivatives appearing in the governing equations. In reference [31], the derivative approximations are expressed in terms of an assembly of submatrices, each of which describes the interactions of wavelets and their derivatives across a range of scales and spatial locations. In the current paper, the accuracy and stability of derivative approximations based on interpolating wavelets are also found. Scaling functions with a large polynomial span are constrained to provide numerical approximations with a formal accuracy less than the maximum attainable for a given computational stencil. It is also found that approximations based on wavelets with a large polynomial span are unstable for non-periodic discretizations. In addition, lifting the MRA does little to improve the situation. The influence of lifting on the numerical implementation and behaviour of our numerical scheme is examined, and found to be comparatively minor.

The theoretical development of wavelets in reacting flows

Abstract This paper focuses on the simulation of turbulent reacting flows via recent developments in wavelet-based analyses. The unique data compression properties of wavelet methods render them especially attractive for such simulations, in which the length and time-scales of interest originate from both physical and chemical processes and may span several orders of magnitude. The particular difficulties encountered when representing reacting flow problems on non-periodic domains, and how these difficulties have led to the adoption of a biorthogonal wavelet framework, are discussed. This leads to consideration of interpolating wavelet transforms based on second-generation wavelets, for which a fast transform algorithm is presented. Issues raised by the application of wavelet transform methods to the reacting Navier-Stokes equations, including the calculation of differential operators, the extension to two and three dimensions and the evaluation of non-linear terms, are examined. The implications of the wavelet approach for the representation of the turbulent energy cascade are explored briefly. Finally, some future directions for research into the extension of wavelet analysis as an underpinning technology for computational fluid dynamics are indicated.

The application of wavelets to reacting flows

Abstract The prospects presented by wavelets in the numerical analysis of chemically reacting turbulent flows are examined. In many flows of industrial relevance, combustion takes place in a stream of turbulent premixed gases. The mode of combustion is said to lie in the laminar flamelet regime. When a combustion process belonging to this regime occurs, it is anticipated that the flow field will be split into two components: reactants, consisting essentially of the fuel-air mixture, and products, typically consisting of carbon dioxide, water vapour, nitrogen and a number of other trace species. The two regions are separated by the flame, which is typically a very small-scale structure containing all of the chemical and molecular transport effects. The length scale disparity between the thin flame and the flow domain as a whole makes efficient discretization with traditional methods difficult, but is ideally suited to the multiresolution paradigm. In this paper, the current state of the art in the application of wavelets to the discretization of turbulent combustion problems is explored. The limitations of the present approaches as well as their strengths are assessed and outstanding problems from both a theoretical and a practical point of view are discussed. Key research directions for future investigations are highlighted.

Behaviour of a Premixed Flame Subjected to Acoustic Oscillations

In this paper, a one dimensional premixed laminar methane flame is subjected to acoustic oscillations and studied. The purpose of this analysis is to investigate the effects of acoustic perturbations on the reaction rates of different species, with a view to their respective contribution to thermoacoustic instabilities. Acoustically transparent non reflecting boundary conditions are employed. The flame response has been studied with acoustic waves of different frequencies and amplitudes. The integral values of the reaction rates, the burning velocities and the heat release of the acoustically perturbed flame are compared with the unperturbed case. We found that the flames sensitivity to acoustic perturbations is greatest when the wavelength is comparable to the flame thickness. Even in this case, the perturbations are stable with time. We conclude that acoustic fields acting on the chemistry do not contribute significantly to the emergence of large amplitude pressure oscillations.