Philippe Spalart

• PhD
• Fellow at The Boeing Company

We exploit the similarity between the mean momentum equation and the mean energy equation and derive transformations for mean temperature profiles in compressible wall-bounded flows. In contrast to prior studies that rely on the strong Reynolds analogy and the presumed similarity between the instantaneous and mean velocity and temperature signals,...

We call classical a transport model in which each governing equation comprises a production term proportional to velocity gradients and terms such as diffusion and dissipation which are built from the internal quantities of the model and are local. They may depend on the wall-normal coordinate y. We consider the layer along a wall in which the tota...

The objective is to provide clear and well-motivated guidance to Machine Learning (ML) teams, founded on our experience in empirical turbulence modeling. Guidance is also needed for modeling outside ML. ML is not yet successful in turbulence modeling, and many papers have produced unusable proposals either due to errors in math or physics, or to se...

We call classical a transport model in which each governing equation comprises a production term proportional to velocity gradients, and terms such as diffusion and dissipation built from the internal quantities of the model and local. They may depend on the wall-normal coordinate y. We consider the layer along a wall in which the total shear stres...

The purpose of the NASA Juncture Flow experiment was to acquire high-quality flowfield details deep in the corner of a wing–body junction specifically for the purpose of computational fluid dynamics (CFD) validation. A truncated DLR F6 wing was used along with a flat-sided fuselage with windows that allowed both laser Doppler velocimetry and partic...

The quadratic constitutive relation was proposed as an extension of minimal complexity to linear eddy-viscosity models in order to improve mean flow predictions by better estimating turbulent stress distributions. However, the successes of this modification have been relatively modest and are limited to improved calculations of flow along streamwis...

No PDF available ABSTRACT We have developed high-fidelity CFD/CAA capability for the prediction of fan tone and broadband noise from an aero-engine. With a zonal URANS—wall-modeled LES approach, referred to as the Improved Delayed Detached Eddy Simulation (IDDES), the entire geometry of NASA's Source Diagnostic Test (SDT) fan rig including the nace...

The capabilities and limitations of the quadratic constitutive relation in computing streamwise corner flows are investigated using publicly-available data from direct numerical simulations of a square duct flow. The increased accuracy of RANS computations which use the quadratic constitutive relation in corner flows is not due to significantly imp...

The new term belongs in the “basic,” free-shear-flow part of the Spalart–Allmaras (SA) model, and extends an idea of the Secundov team, incorporated in the νt-92 model. It detects transverse curvature in the distribution of the eddy viscosity ν~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage...

The Speed Bump flow model was designed by Boeing to provide a mildly three-dimensional flow with separation from a very smooth surface, strongly controlled by the turbulence. Experiments are conducted by several teams, as are simulations, over a range of Reynolds numbers. Direct Numerical Simulations (DNS) are not possible for the full 3D geometry...

This paper presents two enhancements of the efficient broadband time-domain impedance model proposed by Dragna, Pineau, and Blanc-Benon in 2015. It treats lined walls in the framework of the macroscopic concept of locally reacting acoustic impedance, and allows the formulation of the time-domain impedance boundary condition in the form of a set of...

These approaches to the numerical simulation of high-Reynolds-number turbulent flows combine Reynolds-Averaged Navier–Stokes (RANS) elements and Large-Eddy Simulation (LES) elements. This combination can take many forms, and a classification is proposed here along with the various distinctions that need to be made. First, the reasons not to rely on...

Modifications to the quadratic constitutive relations (QCRs) of Spalart (“Strategies for Turbulence Modelling and Simulation,” International Journal of Heat and Fluid Flow, Vol. 21, 2000, pp. 252–263) and Mani et al. (“Predictions of a Supersonic Turbulent Flow in a Square Duct,” AIAA Paper 2013-0860, Jan. 2013) are proposed. These modifications re...

The turbulent boundary layer over a Gaussian bump is computed by direct numerical simulation (DNS) and wall-modeled large eddy simulation (WMLES) of the incompressible Navier-Stokes equations. The two-dimensional bump causes a rapid succession of favorable-to-adverse pressure gradients that leads to shallow separation on the downstream side. At the...

The target is boundary layers at relatively low Reynolds numbers. The correction is simple and only alters the cw2 constant, so that the calibration of the original model in free shear flows and in high-Reynolds-number boundary layers is preserved. Its effect vanishes for momentum-thickness Reynolds number Rθ larger than about 5000, in the flat-pla...

NASA has recently undertaken a very high fidelity, detailed experiment focused on flow separation at the junction of a wing and its fuselage. It is well known that Reynolds-averaged Navier-Stokes (RANS) models, especially linear eddy viscosity models, struggle to predict this type of flow. Since large eddy simulation (LES) models can be considerabl...

Direct numerical simulation (DNS) is used to study a separated and rapidly reattached turbulent boundary layer over an idealized $35^{\circ }$ infinite swept wing. The separation and reattachment are induced by a transpiration profile at fixed distance above the layer, with the pressure gradient applied to a well-defined, fully developed, zero-pres...

The Ffowcs Williams–Hawkings equation is widely used in computational aeroacoustics to post-process unsteady simulations and provide the sound at distances beyond the accurate range of the grid. It distinguishes the monopole/dipole contributions from solid surfaces Σ and that from quadrupoles present in the volume of the fluid. Curle showed that at...

A very convincing experimental paper from TU Delft, of 2016, motivated this joint study. They directly measured a reduction in drag of up to 3% for the developed turbulent boundary layer flowing over an array of shallow dimples, of diameter comparable with the boundary-layer thickness. The Reynolds numbers were not high, but nor marginal either. Ou...

The fan broadband noise of a rotor–stator system representing a turbofan aeroengine is investigated using the improved delayed detached-eddy-simulation approach. The baseline configuration of the NASA source diagnostic test with the entire hard-wall nacelle is simulated at approach and takeoff conditions. In preceding studies, the simulation method...

A range of turbulence models is exercised in the problem of a mature two-dimensional isolated vortex with high circulation Reynolds number, mature meaning that the core size has grown to many times its initial value, and the vortex reaches a self-similar state in which all quantities scale with its outside circulation Γ and its age t. The reasoning...

A family of cases each containing a small separation bubble is treated by direct numerical simulation (DNS), varying two parameters: the severity of the pressure gradients, generated by suction and blowing across the opposite boundary, and the Reynolds number. Each flow contains a well-developed entry region with essentially zero pressure gradient,...

Tone noise from a rotor–stator system representing a turbofan is studied based on high-fidelity unsteady simulations. The baseline configuration of the NASA source-diagnostic-test geometry with the entire hard-wall nacelle is solved by using the unsteady Reynolds-averaged Navier–Stokes equations and the improved delayed detached-eddy simulation at...

The Paper presents the aerodynamic and turbulent aspects of a project devoted to creating and validating a high-fidelity computational-fluid-dynamics-based system for the prediction of the performance and noise associated with the fan/outlet-guide-vane configuration typical of modern turbofan aeroengines. Such a tool will be of significant value fo...

ADES is not a new concept, but it represents a significant evolution from the original or “Natural” DES concept (NDES), and we believe it could become widespread and the basis for turbulence treatment in most high-Reynolds-number applications once the computing power is sufficient. Therefore, its potential and the likely difficulties inherent in it...

We consider fully developed turbulence in straight ducts of non-circular cross-sectional shape, for instance a square. A global friction velocity $\overline{u}_{\unicode[STIX]{x1D70F}}$ is defined from the streamwise pressure gradient $|\text{d}p/\text{d}x|$ and a single characteristic length $h$ , half the hydraulic diameter (shapes with disparate...

The Bachalo-Johnson experiment on an axisymmetric bump has been a primary validation case for turbulence models in shock-boundary-layer interactions since the 1980’s. In the present work, Wall-Modelled Large-Eddy Simulations (WMLES) of this flow were conducted using Improved Delayed Detached-Eddy Simulation (IDDES) as the sub-grid-scale (SGS) and w...

We study turbulent plane Couette-Poiseuille (CP) flows in which the conditions (relative wall velocity ΔU w ≡ 2U w , pressure gradient dP/dx and viscosity ν) are adjusted to produce zero mean skin friction on one of the walls, denoted by APG for adverse pressure gradient. The other wall, FPG for favorable pressure gradient, provides the friction ve...

The possibility of a crucial delay in the transition from RANS to LES in free and separated shear layers within hybrid RANS-LES methods was anticipated, starting in the proposal of Detached-Eddy Simulation in 1997. Its origin (the presence of the so called “grey area” in the vicinity of the RANS-LES interface) is well understood, but despite numero...

The paper presents jet noise computations performed using the original and some recently proposed modified formulations of detached-eddy simulation, based on alternative definitions of the subgrid length-scale and/or a modified version of the subgrid Spalart-Allmaras model, which involves the Wall-Adapting Local Eddy-viscosity model. The modificati...

Direct Numerical Simulation, i.e., numerical integration of the unsteady 3D Navier-Stokes equations is the most rigorous approach to turbulence simulation, which ensures an accurate prediction of characteristics of turbulent flows of any level of complexity. However its application to complex real-life flows, e.g. the flows past airplanes, cars, et...

This article examines the increasingly crucial role played by Computational Fluid Dynamics (CFD) in the analysis, design, certification, and support of aerospace products. The status of CFD is described, and we identify opportunities for CFD to have a more substantial impact. The challenges facing CFD are also discussed, primarily in terms of numer...

The paper addresses the issue of the significant delay of transition from RANS to LES in shear layers, which is known to affect the original version of Detached-Eddy Simulation (DES) on typical anisotropic grids. A common remedy has been to disable the subgrid scale model, leading to Implicit LES (ILES). Here, enhanced versions of DES are proposed...

A Direct Numerical Simulation (DNS) of Couette-Poiseuille flow is presented and analyzed in two ways. First, we test four semi-theoretical proposals for universal behaviour of respectively the velocity, the mixing length, the eddy viscosity, and the turbulence-kinetic-energy production rate. The question is which one may carry over from zero pressu...

The steady incompressible irrotational flow past a three-dimensional body of any shape generates no forces. The historic paradox refers only to drag, but lift is also zero, which has been known but not emphasized. The new material concerns a body with a long constant cross section, such as a train. The final results for forces and moments are very...

An array of co-rotating vortex generators (VG) is placed in a supersonic boundary layer, similar to that on an airliner wing. Direct numerical simulations (DNS) are conducted, with unsteady turbulent content in the incoming boundary layer obtained from the synthetic-turbulence approach of Shur et al. (Flow Turbul. Combust. 93, 63–92, 2014). The RAN...

A numerical study is presented, aimed at evaluating the capability of vortex generators to produce a significant delay of separation and drag reduction in flows past smooth bluff bodies in the transcritical flow regime, with turbulent boundary layers ahead of separation. A fairly large series of steady Reynolds-averaged Navier-Stokes computations i...

We present two novel approaches to improve the behaviour of DES in the region where an attached boundary layer (handled with RANS) flows into a separated shear layer (to be resolved using LES). The approaches aim to be generally-applicable and retain the non-zonal nature of DES. Furthermore, the formulations are local and can be readily implemented...

Results of an experimental study and numerical simulations are presented for the flow in a circular duct with an obstruction plate and an orifice (diaphragm). This is a model of components of an airplane’s Environmental Control System, or ECS. The Reynolds number of the flow is close to that in actual applications. The simulations rest on versions...

The results of large-eddy and similar simulations and acoustic propagation calculations provided by six participants for the Rudimentary Landing Gear (RLG) category of the 2012 BANC-II workshop are analyzed and compared with experimental results. The general conclusion is that industrial accuracy remains elusive, and very significant differences ex...

Wind turbines arranged in a wind plant impact each other through their wakes. Wind plant control is an active research field that attempts to improve wind plant performance by coordinating control of individual turbines to take into account these turbine–wake interactions.In this paper, high-fidelity simulations of a two-turbine fully waked scenari...

A simple realistic model of a high-aspect-ratio wing near stall was developed, which succeeded in predicting the sudden appearance of lift cells, in qualitative agreement with experiment and CFD studies. The model returns spanwise lift distributions with nearly square waves, which conflicts with the lifting-line approximation. It is also dependent...

The paper presents the detailed formulation and validation results of simple and robust procedures for the generation of synthetic turbulence aimed at providing artificial turbulent content at the RANS-to-LES interface within a zonal Wall Modelled LES of attached and mildly separated wall-bounded flows. There are two versions of the procedure. The...

We seek a clear statement of the scaling which may be expected with rigour for transportation or other noise at low Mach numbers M, based on Lighthill's and Curle's theories of 1952 and 1955. In the presence of compact solid bodies, the leading term in the acoustic intensity is of order M6. Contrary to the belief held since that time that it is of...

In this paper we have confirmed that eddy viscosity turbulence models are inadequate to predict secondary vortical flows developed from corners in internal flows. To remedy this shortcoming, we have added the quadratic constitutive relation (QCR) of Spalart to the one-and two-equation SA and SST turbulence models, respectively. The results of QCR w...

A synergistic utilization of computational simulations with experimental measurements is employed to develop dual-stream nozzle geometries that provide jet-noise reduction with the concurrent ability to control the orientation of the jet plumes, so as to minimize the thrust degradation associated with low-noise designs. The geometries consist of ro...

The flow in the far field of an isolated static momentum source is considered, taking into account the entrainment of fluid by the turbulent jet which develops far downstream irrespective of the type of device. The result is a simple analytical model for the irrotational region, which depends only on the thrust applied. This equation is implied by...

Landing-gear noise is predicted by conducting a Detached-Eddy Simulation of the turbulent region, and extrapolating the sound to the far field using the Ffowcs-Williams-Hawkings (FWH) equation. We use the Rudimentary Landing Gear (RLG), as well as two simpler configurations. Our past results conflicted with expectations based on Curle's approximati...

The power output of large wind farms is limited by the downward flux of kinetic energy through the atmospheric boundary layer, as ultimately all available power at turbine altitude is exhausted. This becomes relevant when the power extracted per unit area is sufficiently large, and the atmospheric boundary layer is significantly affected by the win...

The paper presents two new applications of the large-eddy-simulation-based computational-fluid-dynamics/computational-aeroacoustics system established by the authors since 2002 to the prediction of the broadband shock-cell noise generated by imperfectly expanded sonic jets. The first study addresses the effect of Right on characteristics of single...

A four-wheel "rudimentary" landing gear (RLG) truck was designed for public-domain research, with a level of complexity which is manageable in current numerical simulations, and a weak Reynolds-number sensitivity. Experimental measurements of wall-pressure fluctuations are allowing a meaningful test of unsteady simulations with emphasis on noise ge...

We examine drag-reduction proposals, as presented in this volume and in general, first with concrete examples of how to bridge the distance from pure science through engineering to what makes inventions go into service; namely, the value to the public. We point out that the true drag reduction can be markedly different from an estimate based simply...

The paper highlights major outcomes of a more than 15-year tight collaboration between scientists and engineers of Boeing Commercial Airplanes (Seattle) and a group of scientists from St.-Petersburg under the aegis of the Moscow Boeing Technical Research Center. The collaborative research covers a wide spectrum of basic and applied aerodynamic prob...

An efficient recycling algorithm is developed for injecting resolved turbulent content in a boundary layer as it switches from a Reynolds Averaged Navier-Stokes (RANS) type treatment to a Large Eddy Simulation (LES) type treatment inside a generalized Detached-Eddy Simulation (DES). The motivation is to use RANS in the thinnest boundary-layer area,...

The law of the wall and its companion the logarithmic law are at the center of our knowledge of wall turbulence, and after almost a century still the subject of intense speculation and proposed amendments, based on experimental and simulation results, as well as putative theories. In particular, the consensus over the value of the Karman constant k...

An overview is presented of a non-empirical CFD/CAA numerical system for jet noise prediction developed by the joint US - Russia team since 2002. Key elements of the system are discussed and examples are considered of its application to flow and noise computation for a wide range of cases that progress in the direction of the complete simulation of...

A few years ago we introduced a nomenclature for grid regions in Detached-Eddy Simulations (DES) of external flows: the RANS, Focus, Euler, and Departure Regions (Spalart 2001). These may help organize grid generation and error estimation/reduction. We have four purposes here: to point out that most of these concepts apply to LES, if not to DNS, an...

A four-wheel landing gear truck was designed for research purposes, with the level of complexity which is felt to be manageable in current numerical simulations, and a weak Reynolds-number sensitivity. An experiment is underway, aimed at measuring wallpressure fluctuations, leading to a meaningful test of unsteady simulations with emphasis on noise...

The Large-Eddy Simulation (LES) numerical system established since 2002 for jet-noise computation is first evaluated in terms of recent gains in accuracy with increased computer resources, and is then used to explore the relatively new “microjet” noisereduction concept (injection of high-pressure microjets in the vicinity of the main jet nozzle exi...

Results of RANS and Delayed Detached Eddy Simulation (DDES) are presented for a new research model of landing gear. The design is as simple as that of Lazos but a primary motivation for it is a weak and well-understood Reynolds-number dependence. The simplicity should allow essentially grid-converged RANS-LES solutions now or within a few years, bu...

The article begins with a reminder that the need for RANS modelling in 2009 is not any lower than had been predicted in 1997, when Detached-Eddy Simulation was created against a wave of predictions that Large-Eddy Simulation (LES) would soon make RANS redundant. The CFD community, in large part, has embraced DES and other hybrid RANS-LES approaches...

The paper presents two new applications of the LES-based CFD/CAA system established by the authors since 2002, to the prediction of the broadband shock-cell (BBSC) noise generated by imperfectly expanded sonic jets. The first study addresses the effect of flight on the flow and noise characteristics of single under-expanded sonic jets, and the seco...

Counter-rotating open rotors, as proposed for future airliners, are treated by an Unsteady Reynolds-Averaged Navier-Stokes (URANS) method, with body-fitted sliding grid blocks. The far-field sound is then calculated using the Ffowcs-Williams-Hawkings equation, applied on a permeable surface. A generic set of rotors of equal diameter created manuall...

Wall-bounded turbulence in pressure gradients is studied using direct numerical simulation (DNS) of a Couette–Poiseuille flow. The motivation is to include adverse pressure gradients, to complement the favourable ones present in the well-studied Poiseuille flow, and the central question is how the scaling laws react to a gradient in the total shear...

A detailed investigation of detached-eddy simulation (DES) applied to the flow around nominally 2D airfoils in deep stall has been conducted. The sensitivity of the flow to a wide range of computational parameters has been assessed. The principal parameters of influence were found to be the length of the time sample computed for Reynolds averaging...

The paper presents an overview of the authors contribution to the BANC-I Workshop on the flow past tandem cylinders (Category 2). It includes an outline of the simulation approaches, numerics, and grid used, the major results of the simulations, their comparison with available experimental data, and some preliminary conclusions. The effect of varyi...

Direct numerical simulation (DNS) is used to study the effects of mean lateral divergence and convergence on wall-bounded turbulence, by applying uniform irrotational temporal deformations to a plane-channel domain. This extends a series of studies of similar deformations. Fast and slow straining fields are considered, leading to a matrix of four c...

A retraction of our findings in Ref. [1] is necessary. The numerical accuracy was not up to the required standards, allowing an error of about 0.3 in U+ in the buffer layer, and was insufficient to support the logarithmic law that was proposed. New results on two levels of finer grids are presented and found to be close, and to compare very well wi...

The Large-Eddy Simulation (LES) system established over the last six years is reviewed in terms of its progress in accuracy and transition physics, and is then used to explore the transmission of noise from a known local source through a turbulent region, here the shear layer of a jet. For this, weak artificial monopole sources are added to an LES,...

The Ffowcs Williams - Hawkings (FWH) equation is often used in an inexact manner in numerical settings, because the amount of information available is limited. Generally the volume integral, or quadrupole term, is omitted even though the (permeable) FWH surface fails to enclose the turbulence region, which is unmanageably long for jet or bluff-body...

The goal of this work is the prediction of the far-field noise produced by a flap edge using Detached Eddy Simulation (DES) coupled with a Ffowcs-Williams Hawkings (FWH) integral. Flap edges are an important noise source for airliners in approach. A DES of the complete aircraft would be far too costly on current computers and the problem size has b...

The behaviors of the widely used Spalart-Allmaras and Menter shear-stress transport turbulence models at low Reynolds numbers and under conditions conducive to relaminarization are documented. The flows used in the investigation include 2-D zero-pressure-gradient flow over a flat plate from subsonic to hypersonic Mach numbers, 2- airfoil flow from...

Some aircraft have exhibited a noticeable vibration and aero-acoustic phenomenon inside the nose landing gear cavity. The goal of the present study was to determine whether unsteady CFD using either unsteady RANS or detached eddy simulation (DES) could predict the cavity oscillation that was measured in a Boeing wind tunnel test. In general the agr...

A few years ago we introduced a nomenclature for grid regions in Detached- Eddy Simulations (DES) of external flows: the RANS, Focus, Euler, and Departure Regions 1. These may help organize grid generation and error estimation/reduction. We have four purposes here: to point out that most of these concepts apply to LES, if not to DNS, and are not tr...

Detached-eddy simulation (DES) was first proposed in 1997 and first used in 1999, so its full history can be surveyed. A DES community has formed, with adepts and critics, as well as new branches. The initial motivation of high– Reynolds number, massively separated flows remains, for which DES is con-vincingly more capable presently than either uns...

A CFD strategy is proposed that combines delayed detached-eddy simulation (DDES) with an improved RANS-LES hybrid model aimed at wall modelling in LES (WMLES). The system ensures a different response depending on whether the simulation does or does not have inflow turbulent content. In the first case, it reduces to WMLES: most of the turbulence is...

Results at Ekman Reynolds numbers Re ranging from 1000 to 2828 expand the direct numerical simulation (DNS) contribution to the theory of wall-bounded turbulence. An established spectral method is used, with rules for domain size and grid resolution at each Reynolds number derived from the theory. The Re increase is made possible by better computer...

The local (pointwise) entropy generation rate per unit volume S‴ is a key to improving many energy processes and applications. Consequently, in the present study, the objectives are to examine the effects of Reynolds number and favorable streamwise pressure gradients on entropy generation rates across turbulent boundary layers on flat plates and -...

A set of matched asymptotic expansions is proposed for the flow far behind an aircraft, with the primary purpose of identifying lift, thrust and drag, particularly induced drag, in a unified manner in integral statements of the momentum equation. The fluid in the far wake is inviscid and incompressible, and variations of total pressure are allowed,...

Numerical simulations of the flowfield and noise of single and staggered dual, round, and beveled nozzles are carried out, with the goal of gaining insights into the flow features that are responsible for noise generation and mitigation, and ultimately arriving at better designs. For aircraft applications, the geometry of the nozzles must be satisf...