Guido S. Baruzzi

A finite element method study of Eulerian droplets impingement models

To compute droplet impingement on airfoils, an Eulerian model for air flows containing water droplets is proposed as an alternative to the traditional Lagrangian particle tracking approach. Appropriate boundary conditions are presented for the droplets equations, with a stability analysis of the solution near the airfoil surface. Several finite element formulations are proposed to solve the droplets equations, based on conservative and non-conservative forms and using different stabilization terms. Numerical results on single and multi-elements airfoils for droplets of mean volume diameter, as well as for a Langmuir distribution of diameters, are presented and validated against measured values

FENSAP-ICE-Unsteady: Unified In-Flight Icing Simulation Methodology for Aircraft, Rotorcraft, and Jet Engines

In-flight ice accretion, even though driven by a steady flow airstream, is an inherently unsteady phenomenon. It is, however, completely ignored in icing simulation codes (one-shot) or, at best approximated via quasi-steady modeling (multishot). The final ice shapes thus depend on the length of the total accretion time (one-shot), or of the arbitrarily prescribed time intervals (multishot), during which the impact of ice growth on both airflow and water impingement is ignored. Such a longstanding heuristic approximation is removed in this paper by coupling in time the dilute two-phase flow (air and water droplets flow) with ice accretion, and is implemented in a new code, FENSAP-ICE-Unsteady. The two-phase flow is solved using the coupled Navier–Stokes and water concentration equations, and the water film characteristics and ice shapes are obtained from laws of conservation of mass and energy within the thin film layer. To continually update the geometry of the iced surface in time, arbitrary Lagrangian–Eulerian terms are added to all governing equations to account for mesh movement in the case of stationary components. In the case of rotating/stationary interacting components, a dynamically stitched grid is used. The numerical results clearly show that unsteady modeling improves the accuracy of both rime and glaze ice shape prediction, compared with the traditional quasi-steady approach with frozen solutions. The unsteady model is shown to open the door for a unified approach to icing on fixed wings, on helicopters with blades/rotors/fuselage systems. Problems of current concern in the icing community such as the ingestion of ice crystals at high altitude become tractable with the new formulation.

FENSAP-ICE: Analytical Model for Spatial and Temporal Evolution of In-Flight Icing Roughness

Ice roughness, which has a major influence on in-flight icing heat transfer and, hence, ice shapes, is generally input from empirical correlations to numerical simulations. It is given as uniform in space, while sometimes being varied in time. In this paper, a predictive model for roughness evolution in both space and time during in-flight icing is presented. The distribution is determined mathematically via a Lagrangian model that accounts for the stochastic process of bead nucleation, growth, and coalescence into moving droplets and/or rivulets and/or water film. This general model matches well the spatial and temporal roughness distributions observed in icing tunnel experiments and is embedded in FENSAP-ICE, extending its applicability outside the range of airfoil types for which correlations exist. Thus, an additional important step has been taken toward removing another empirical aspect of in-flight icing simulation.

FENSAP-ICE: Ice Accretion in Multi-stage Jet Engines

Ice accretion in aircraft engine components has raised safety and performance concerns. When flying in hazardous weather conditions, engines can ingest a mix of iced and liquid particles that can potentially result in a dangerous build-up on the forward components of the engines. The ice can then shed from the fan, spinner or IGV, and may cause mechanical damage and performance losses to downstream components. In order to cost-effectively replicate such an environment, a three-dimensional quasi-steady numerical approach is developed to model both rotating and static components, and their interaction. An inter- component mixing-plane approach, along with stagnation and radial equilibrium boundary conditions, has been implemented within FENSAP-ICE allowing the treatment of multi- stage unequal-pitch blade rows via a finite element interpolation method and proper circumferential averaging. The approach is first validated for the well-documented Aachen turbine and then used on a compressor stage to obtain impingement locations of supercooled droplets and ice shapes.

FENSAP-ICE: Unsteady Conjugate Heat Transfer Simulation of Electrothermal De-Icing

DOI: 10.2514/1.C031607 This paper presents a truly unsteady approach for the numerical simulation of in-flight electrothermal anti-icing orde-icing, using a conjugate heat transfer technique. This numerical approach has been implemented in FENSAPICE to compute the complex heat transfer phenomena occurring during in-flight de-icing with multiple heating elements following independent cycling. At each time step, the energy fluxes through the aircraft’s solid skin, the melting ice layer, the liquid water film, and the external fluid are computed. The ice shape is then modified by taking intoaccounttheopposingmassbalanceeffectsoficeaccretingduetotheimpactofsupercooleddropletsand/orwater runback, and the partial or total melting of the existing ice layer due to heating. The results of the verification of this phase-changeconductioncodearepresented,followedbyastudyofintercyclede-icingonawing,showingintercycle ice growth. Nomenclature ch = convective heat flux coefficient d = droplet diameter E = internal energy e = volumetric internal energy H = enthalpy

FENSAP-ICE: Modeling of Water Droplets and Ice Crystals

A series of high-altitude turbofan engine malfunctions characterized by flameouts and rollbacks have been reported in recent years. The source of these incidents has been related to the presence of ice crystals at high altitudes and, consequently, to a dangerous ice build-up engine components found upstream. Ice can then shed and may cause mechanical damage and performance losses to downstream components. In order to provide a numerical tool to analyze such situations, FENSAP-ICE has been extended to model mixed-phase flows that combine air, water and ice crystals, and the related ice accretion. The approach is validated against test results from the Cox & Co. Icing Tunnel.

FENSAP-ICE Simulation of Complex Wind Turbine Icing Events, and Comparison to Observed Performance Data

A numerical simulation of a complex wind turbine icing event is performed using the FENSAP-ICE simulation system. First, 2D and 3D simulations of a characteristic atmospheric icing event on a small wind turbine are compared to experimental data. Comparable results are obtained with both methods, supporting the use of the 2D blade section approach for more computationally intensive simulations, which would be prohibitively expensive in 3D. A complex, historical weather event is then simulated on an industrial-scale wind turbine. The selected weather event is 17 hours long and based on data collected at a wind farm in the Gaspe Peninsula, Quebec, Canada. Since the actual turbine geometry was not available, the WindPACT 1.5 MW wind turbine rotor was selected for use in the simulations as it is of comparable size and rating to the wind turbines located on the Gaspe site. The performance simulation of the contaminated turbine compares well to the characteristics of the actual contaminated turbines at the Gaspe wind farm.

Simulation of Supercooled Large Droplet Impingement via Reduced Order Technology

A IRCRAFT flying through clouds of supercooled liquid droplets (SLD) can be subjected to in-flight ice accretion. Surface tension prevents the expansion of the droplets that would occur with phase change, forcing them to remain in liquid form even though their temperature is below the freezing point. When the droplets hit an aircraft’s surfaces, the surface tension decreases at the contact point, and theymay freeze completely on impact if the temperature is very low or freeze partially at higher temperatures, whereas the remaining liquid portion runs back on the surface, transported by the pressure gradient and the shear stress of the airflow. If no ice protection is provided, the aerodynamic characteristics of the aircraft and its handling can be severely degraded when ice accretes. The increased drag generated by the roughness of the ice can lead to flow separation, reduction of the stall margins, control reversals, and engine blockages [1]. Airworthiness of transport airplanes in icing conditions is demonstrated by compliance with certification standards (Appendix C of the FAA Federal Aviation Regulations, part 25) set by agencies, such as the Federal Aviation Administration, European Air Safety Association, Transport Canada, etc. These standards, frozen for 50 years, will soon undergo significant revisions with the adoption of Appendix O to address the icing threat posed by SLD conditions. Unlike smaller droplets, SLD can distort, break into smaller droplets, splash, bounce off surfaces, get carried downstream by the flow, and reimpinge, increasing the potential for ice contamination on unprotected surfaces [2–4]. Nowadays, wind tunnel tests, icing tunnel tests, and computer simulations play major complementary roles in the process of certifying a new aircraft [5,6]. Advances in modeling capabilities have created the conditions to accurately simulate the ice accretion process in a realistic three-dimensional (3-D) context [7,8]. Unfortunately, the computational cost associated with performing a multitude of 3-D simulations of various aeroicing conditions somewhat limits the widespread use of computational fluid dynamics (CFD), even if advanced computational resources are available [9,10]. To overcome this difficulty, mostly low-cost and, consequently, low-fidelity tools are usually employed. These may be based on empirical correlations, two-dimensional (2-D) approximations, inviscid or incompressible flow assumptions, and/or other simplifications that result in limited accuracy and realism. A viable alternative is the reduced-order modeling (ROM) approach [11,12], which dramatically reduces the cost of highfidelity simulations while providing solutions of superior accuracy to low-fidelity methods because it preserves the detailed physical modeling of the problem under consideration [13–16]. Although the use of this approach in the aeroicing environment is in its pioneering phase, recent results support the effectiveness of this methodology as a valuable tool in the context of a multicondition, multiparameter certification process [17–20]. In a framework of ice accretion simulation as the succession of airflow, water concentration, and heat transfer calculations, the most time-consuming part is obtaining the water impact patterns. The common practice is to assume a distribution of discrete droplet diameters, compute the impingement distribution of each diameter class, andweight-average thesemonodispersed solutions. In the case of the droplet sizes of Appendix C, seven distinct monodispersed sizes (Langmuir-D distribution) are used to compute the overall impingement distribution. In the SLD regime, however, due to the complex phenomena of droplet breakup, splashing, and bouncing, distributions containing up to 27 diameters of monodispersed droplets are needed to obtain realistic impingement predictions [5–7]. The computational cost of an SLD simulation is hence four times that of a Langmuir-D distribution. In the presentwork, it will be shown that the ROM approach can dramatically reduce cost with only a very modest degradation of the overall accuracy of the simulation. The essentials of the ROM approach used to extract the solution eigenfunctions (or modes) and compute solutions at unknown states are introduced in sections II and III of this paper, whereas section IV illustrates the interpolation technique used to compute the surrogate solutions. Finally, 2and 3-D results and comparison with experiments and other methods are presented to validate the present methodology. Received 29 July 2011; revision received 14 September 2011; accepted for publication 15 September 2011. Copyright

FENSAP-ICE: Application of Unsteady CHT to De-icing Simulations on a Wing with Inter-cycle Ice Formation

A truly unsteady approach for the numerical simulation of in-flight electro-thermal antiicing or de-icing using a Conjugate Heat Transfer (CHT) technique is presented. This numerical approach has been implemented in FENSAP-ICE to compute the complex heat transfer phenomena occurring during in-flight de-icing with multiple heating elements. At each time step, the energy fluxes through the aircraft solid skin, the melting ice layer, the liquid water film and the external fluid are computed. The ice shape is then modified by taking into account the mass balance of ice accreting due to the impact of supercooled droplets and water runback, and the melting of the ice layer due to heating. The results of the verification of the phase-change conduction code are presented, followed by a study of inter-cycle de-icing on a wing using CHT, showing inter-cycle ice growth.

Quasi-molecular modeling of supercooled large droplets dynamics for in-flight icing simulations

A fine-scale model of Supercooled Large Droplets dynamics is proposed based on a quasi-molecular approach, a meso-scale method that mimics the interaction between quasimolecules within a single liquid droplet. Each quasi-molecule is a combination of a large number of real molecules which are considered to be an ensemble. The goal is to simulate the deformation and the splashing processes of a droplet to obtain a better understanding of the dynamics of large droplets collisions with aircraft at realistic flight conditions in order to refine the macroscopic Eulerian description of the process.