Carmine De Bartolo

Up to sixth-order accurate A-stable implicit schemes applied to the Discontinuous Galerkin discretized Navier–Stokes equations

Abstract In this paper a high-order implicit multi-step method, known in the literature as Two Implicit Advanced Step-point (TIAS) method, has been implemented in a high-order Discontinuous Galerkin (DG) solver for the unsteady Euler and Navier–Stokes equations. Application of the absolute stability condition to this class of multi-step multi-stage time discretization methods allowed to determine formulae coefficients which ensure A-stability up to order 6. The stability properties of such schemes have been verified by considering linear model problems. The dispersion and dissipation errors introduced by TIAS method have been investigated by looking at the analytical solution of the oscillation equation. The performance of the high-order accurate, both in space and time, TIAS-DG scheme has been evaluated by computing three test cases: an isentropic convecting vortex under two different testing conditions and a laminar vortex shedding behind a circular cylinder. To illustrate the effectiveness and the advantages of the proposed high-order time discretization, the results of the fourth- and sixth-order accurate TIAS schemes have been compared with the results obtained using the standard second-order accurate Backward Differentiation Formula, BDF2, and the five stage fourth-order accurate Strong Stability Preserving Runge–Kutta scheme, SSPRK4.

Experimental and Numerical Investigation on the Effects of the Seeding Properties on LDA Measurements

The characteristics of the seeding particles, which are necessary to implement the laser Doppler anemometry (LDA) technique, may significantly influence measurement accuracy. LDA data were taken on a steady-flow rig, at the entrance of the trumpet of the intake system of a high-performance engine head. Five sets of measurements were carried out using different seeding particles: samples of micro-balloons sieved to give three different size ranges (25-63 μm, 90-200 μm, and standard as received from the manufacturer 1-200 μm), smoke from a home-made sawdust burner (particle size ≤1 μm), and fog from a commercial device (particle size around 1 μm). The LDA data were compared with the results of two-phase computational fluid dynamics simulations.

The Separation Between Turbulence and Mean Flow in ICE LDV Data: The Complementary Point-of-View of Different Investigation Tools

LDV measurements have been taken in a disc chamber four-stroke reciprocating engine under motoring conditions, Two non-simultaneous velocity components have been recorded at three different locations on the mid-plane of the TDC clearance during the intake and compression strokes for three different speeds (600, 800, 1000 rpm). The locations are characterized by different flow conditions (near the intake valves; on the cylinder axis; near the exhaust valves). The combination of different engine speeds and different chamber locations enables one to look both at the global behavior of the flow and at the details of the turbulence time-evolution. The aim of the research is to identify the frequency which can be considered a separation between true turbulence and cycle-by-cycle variation of the mean flow and to analyze the variation of such a frequency with the measuring location and with the engine speed. The analysis has been carried out by using different tools: the non-stationary velocity autocorrelation function, the power spectrum and the cycle-resolved analysis based on the frequency filter. The various approaches offer complementary perspectives of the same phenomenon, which give a clear perception of the physical meaning of the most frequently used investigation tools. The results show that the cut-off frequency increases as the engine speed increases and as the measuring point moves away from the ordered jet coming out of the intake valves.

Simulation and experimental validation of the flow field at the entrance and within the filter housing of a production spark-ignition engine

Abstract The paper aims to analyse the flow field at the entrance and within the filter housing of a production four-cylinder, spark-ignition engine during the intake phase. To this purpose a computational fluid dynamic (CFD) analysis was carried out adopting a finite volume code, while an experimental activity was performed at a steady flow rig to validate the computational model. The comparison between numerical data and experimental measurements showed a good agreement and it demonstrated the capabilities of the proposed CFD model to predict in detail the flow field within a complex production automobile component that largely influences the efficiency and reliability of actual internal combustion engines (ICEs).

Numerical and Experimental Analysis of the Intake Flow in a High Performance Four-Stroke Motorcycle Engine: Influence of the Two-Equation Turbulence Models

An experimental and numerical analysis of the intake system of a production high performance four-stroke motorcycle engine was carried out. The aim of the work was to characterize the fluid dynamic behavior of the engine during the intake phase and to evaluate the capability of the most commonly used two-equation turbulence models to reproduce the in-cylinder flow field for a very complex engine head. Pressure and mass flow rates were measured on a steady-flow rig. Furthermore, velocity measurements were obtained within the combustion chamber using laser Doppler anemometry (LDA). The experimental data were compared to the numerical results using four two-equation turbulence models (standard k-e, realizable k-e, Wilcox k-w, and SST k-ω models). All the investigated turbulence models well predicted the global performances of the intake system and the mean flow structure inside the cylinder. Some differences between measurements and computations were found close to the cylinder head while an improving agreement was evident moving away from the engine head. Furthermore, the Wilcox k-w model permitted the flow field inside the combustion chamber of the engine to be reproduced and the overall angular momentum of the flux with respect to the cylinder axis to be quantified more properly.

Influence of Valve Lift and Throttle Angle on Intake Flow in a High-Performance Four-Stroke Motorcycle Engine

A high-performance four-stroke motorcycle engine was analyzed at a steady flow rig. The aim of the work was to characterize the fluid dynamic behavior of the engine head during the intake phase. To this purpose a twofold approach was adopted: the dimensionless flow coefficient was used to evaluate the global breathability of the intake system, while the laser doppler anemometry (LDA) technique was employed to define the flow structure within the combustion chamber. The analysis gave evidence of two contrarotating vortices with axes parallel to the cylinder axis and showed variations in the flow structure when moving away from the engine head. Furthermore, the study highlighted the great influence of the throttle angle on the head fluid dynamic efficiency and how this influence changes with the valve lift. Experimental data were correlated by a single curve adopting a new dimensionless plot. Moreover, LDA measurements were used to evaluate the angular momentum of the flux and an equivalent swirl coefficient, and to correlate them to a previous global swirl characterization carried out on the same engine head using an impulse swirl meter.

High-Order Discontinuous Galerkin Solution of Unsteady Flows by Using an Advanced Implicit Method

The aim of this paper is to investigate and evaluate a multi-stage and multi-step method that is an evolution of the more common Backward Differentiation Formulae (BDF). This new class of formulae, called Two Implicit Advanced Step-point (TIAS), has been applied to a high-order Discontinuous Galerkin (DG) discretization of the Navier-Stokes equations, coupling the high temporal accuracy gained by the TIAS scheme with the high space accuracy of the DG method. The performance of the DG-TIAS scheme has been evaluated by means of two test cases: an inviscid isentropic convecting vortex and a laminar vortex shedding behind a circular cylinder. The advantages of the high-order time discretization are illustrated comparing the sixth-order accurate TIAS scheme with the second-order accurate BDF scheme using the same spatial discretization.

MATRIX-FREE MODIFIED EXTENDED BACKWARD DIFFERENTIATION FORMULAE APPLIED TO THE DISCONTINUOUS GALERKIN SOLUTION OF COMPRESSIBLE UNSTEADY VISCOUS FLOWS

In this work a matrix-free modified extended backward differentiation time integration method has been implemented in a high-order discontinuous Galerkin solver for the unsteady Navier-Stokes equations. The resulting non-linear systems at each time step are solved iteratively using a preconditioned inexact Newton/Krylov method. In order to speed-up the solution process a frozen preconditioner formulation and a polynomial extrapolation technique for computing a better initial guess for the Newton iterations have been considered. Numerical results for compressible inviscid and viscous test cases show the effectiveness of the proposed numerical strategies and the performance advantages of the matrix-free method compared to its matrix-explicit counterpart for this class of implicit multi-stage time schemes. Furthermore, the influence of some physical (low Mach) and space discretization (stretched grid) aspects is examined to highlight pros and cons of the proposed time integration algorithm and its potential in solving non-stiff and stiff systems with respect to the widely used explicit Runge-Kutta schemes.