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News editors obtained the following quote from the background information supplied by the inventors: "This invention relates to the general domain of aerodynamics and concerns digital simulation of aerodynamic flows for an aircraft.

"Its application lies in the aeronautic field for which the design of an aircraft requires precise knowledge of aerodynamic coefficients associated with its various elements.

"When designing an aircraft, an attempt is made to determine global aerodynamic coefficients associated with its various elements, for example coefficients associated with the wings such as lift, drag and the pitching moment.

"These coefficients can be determined in different ways, particularly by digital simulation of fluid flows that consists of analysing movements of a fluid or the effects of these movements by digital solution of equations governing the fluid.

"A digital model is chosen to reproduce the fluid flow in a zone in space that surrounds an element of the aircraft. This zone in space is called the geometric domain of the fluid or calculation domain.

"Digital simulation is used to determine physical values (for example speed, pressure, temperature, density, etc.) for each point in the calculation domain, for a global cost usually much lower than wind tunnel or flight tests.

"The equations to be solved can be very varied depending on the chosen approximations that are usually the result of a compromise between the need for a physical representation and the calculation load, the equations most frequently used being Euler equations (representing a non-viscous adiabatic fluid) and Navier-Stokes equations (representing a viscous heat conducting fluid). Navier-Stokes equations are usually averaged and complemented by turbulence models.

"These equations are digitally solved by computers, using meshes discretising the geometric domain of the fluid to be studied and digital schemes that replace the continuous form of equations by discrete forms. This solution is usually made iteratively, in other words starting from an initial state (for example corresponding to a uniform flow) and performing successive calculation iterations consisting of calculating the next state from the current state.

"Ideally, this iterative method should lead to a state that no longer changes as more iterations are carried out and corresponds to a rigorous solution of discretised equations. In practice, this state is not achieved regardless of the number of iterations made and the simulation has to be stopped as a function of specific criteria, for example after reaching a number of iterations fixed in advance or when the difference between two successive states is less than a given quantity.

"The convergence quality of a digital simulation of aerodynamic flows can be evaluated based on plots of changes to aerodynamic coefficients made at a linear scale. The values of an aerodynamic coefficient can be positive, negative or zero and their convergence towards a previously unknown value is studied.

"The use of a linear scale for the plot of the change to aerodynamic coefficients combined with the fact that this change normally converges, results in a plateau being obtained on the plot of the curve, which is interpreted as a demonstration of convergence.

"Nevertheless, with this type of plot, it is difficult to see precisely how these coefficients change in the plateau, which makes a precise analysis of the simulation convergence more difficult.

"Zooms of the plot then have to be made frequently, but this has the disadvantage of requiring manual work to use plotting software and a large calculation workload. Furthermore, these zooms are impossible if all that is available are plots printed on paper.

"The purpose of this invention is to disclose a method for simulating fluid flows to determine changes to aerodynamic coefficients correcting the above-mentioned disadvantages."

As a supplement to the background information on this patent application, VerticalNews correspondents also obtained the inventor's summary information for this patent application: "This invention is defined by a computer method of simulating a fluid flow in an aircraft environment to determine at least one aerodynamic coefficient characterising the aerodynamic behaviour of at least one element of the aircraft, said method comprising a digital solution of equations modelling the fluid flow in said environment, according to a model configured using physical parameters of the fluid, said digital solution being made iteratively to obtain a first series of values of the aerodynamic coefficient indexed by the number of iterations, said method also comprising the following steps: defining a criterion for convergence of said aerodynamic coefficient, selecting a determined set of terms belonging to said first series of values of the aerodynamic coefficient, as a function of said convergence criterion, defining a monotonic function configured to make a relatively expanding transformation in said determined set relative to the complement of said set; applying said monotonic function on said first series to form a second series of values of the aerodynamic coefficient, said second series defining a global change to said aerodynamic coefficient with a local expansion in a convergence zone corresponding to said determined set; determining said aerodynamic coefficient by plotting a variation curve representative of said second series of values of the aerodynamic coefficient as a function of the number of iterations, and displaying said variation curve including an intrinsic zoom (or magnification) of said convergence zone giving details of the convergence of said aerodynamic coefficient.

"Thus, the method is capable of globally analysing changes to the aerodynamic coefficient, while making a detailed analysis of its behaviour in the attraction or convergence zone. This makes it possible to quickly and very precisely evaluate the stationary value of the aerodynamic coefficient and the degree of convergence of the digital simulation. It is no longer necessary to make magnifications to determine the aerodynamic coefficient.

"According to one aspect of this invention, said convergence criterion is defined as a function of a predetermined number of iterations.

"This can give a direct magnification in the zone of interest to provide a more adapted curve.

"According to another aspect of this invention, said predetermined number of iterations corresponds to a total number of iterations.

"When the total number of iterations fixed in advance is reached, the solution becomes closer and closer to convergence, in other words to the stationary state of the real flow.

"Advantageously, the cardinality of said determined set is defined as a function of a predetermined order of magnitude of the aerodynamic coefficient.

"This means that the simulation can be detailed in a zone for which the extent and precision are chosen based on considerations about the type and expected order of magnitude of the aerodynamic coefficient.

"Advantageously, said monotonic function corresponds to a mixed linear-logarithmic transformation with a linear behaviour in said determined set and a logarithmic behaviour outside said determined set defined as follows:

"F(x)=x/10.sup.psi|x|.ltoreq.10.sup.p and

"F(x)=sign(x)log.sub.10(|x|/10.sup.p-1)si|x|>10.sup.p,

"where p is an order of magnitude of precision.

"This mixed linear-logarithmic transformation has the advantage of facilitating implementation and familiarity of interpretation for users.

"Advantageously, the method comprises the addition of a constant to each term in the first series before application of said monotonic function, said constant being equal to the value of the aerodynamic coefficient at said determined number of iterations.

"This further facilitates the evaluation of the convergence of the aerodynamic coefficient by making the series tend towards zero.

"Advantageously, the method also comprises the application of an absolute value operation on the terms of said second series to form a third series of positive terms.

"This simplifies determination of convergence of the aerodynamic coefficient.

"Advantageously, the method also comprises the following steps:

"applying an oscillation filtering operation on said third series to form a fourth monotonic series; and

"plotting a positive and monotonic variation curve representative of said fourth series.

"According to one example of this invention, the method comprises the following steps:

"plotting a preliminary variation curve C0(I) representative of said first series of values of the aerodynamic coefficient as a function of the number of iterations;

"defining at least one interval of values of the aerodynamic coefficient corresponding to said determined set;

"applying said mixed linear-logarithmic monotonic function on said preliminary variation curve operating a linear transformation inside said interval and a logarithmic transformation outside said interval to form said variation curve.

"According to one embodiment of this invention, the method comprises the following steps:

"calculating a final value C.sub.0final=C.sub.0(I.sub.max), a maximum value C.sub.0max=max(C.sub.0(I)), and a minimum value C.sub.0min=min(C.sub.0(I)) of said preliminary variation curve C.sub.0(I)

"recursively defining a fifth decreasing series I.sub.0.sup.p, I.sub.0.sup.p+1, . . . , I.sub.0.sup.i, . . . , I.sub.0.sup.m-1, I.sub.0.sup.m such that I.sub.0.sup.i>C.sub.0min.A-inverted.i.epsilon.[p, m-1], I.sub.0.sup.m.ltoreq.C.sub.0min, I.sub.0.sup.p=M.sub.0.sup.p-10.sup.p, and M.sub.0.sup.p.apprxeq.C.sub.0final to the nearest 10p, where p is an order of magnitude of precision,

"recursively defining a sixth increasing series S.sub.0.sup.p, S.sub.0.sup.p+1, . . . , S.sub.0.sup.i, . . . , S.sub.0.sup.n-1, S.sub.0.sup.n, such that S.sub.0.sup.i

"defining a seventh ordered series as a function of said fifth and sixth series: I.sub.0.sup.m

"defining a lower interval, [I.sub.0.sup.mI.sub.0.sup.p], a median interval [I.sub.0.sup.p, S.sub.0.sup.p], and an upper interval [S.sub.0.sup.p, S.sub.0.sup.n],

"applying said mixed linear-logarithmic monotonic function on said preliminary variation curve using said seventh ordered series to form said variation curve as follows:

"C.sub.2'(I)=F(C.sub.0(I)-M.sub.0.sup.p)

"I.sub.2.sup.i=F(I.sub.0.sup.i-M.sub.0.sup.p).A-inverted.i.epsilon.[p,m]

"S.sub.2.sup.i=F(S.sub.0.sup.i-M.sub.0.sup.p).A-inverted.i.epsilon.[p,n]

"M.sub.2.sup.p=F(M.sub.0.sup.p-M.sub.0.sup.p)=F(0)=0.

"According to another embodiment of this invention, the method comprises the following steps:

"translating said preliminary variation curve by the value of the aerodynamic coefficient at the total number of iterations to form an intermediate variation curve,

"determining a high order of magnitude m relative to said intermediate variation curve, defined as being the relative integer m such that:

"10.sup.m-1

"defining said interval by extremities equal to -10p and 10p where p is an order of magnitude of precision that is strictly less than said high order of magnitude m, and

"applying said mixed linear-logarithmic monotonic function on said intermediate variation curve using said ordered series to form said variation curve as follows:

"C.sub.2'(I)=C.sub.1(I)10.sup.-p for |C.sub.1(I)|.ltoreq.10.sup.p, and

"C.sub.2'(I)=sign(C.sub.1(I))[log.sub.10(|C.sub.1(I)|)-p+1] for |C.sub.1(I)|>10.sup.p.

"Advantageously, the method comprises the following steps:

"applying an absolute value on said variation curve to form a positive variation curve C3(I), and

"plotting a positive monotonic variation curve C4(I) using a recurrence calculation for I decreasing between

"C.sub.4(I.sub.max)=C.sub.3(I.sub.max)

"C.sub.4(I)=max(C.sub.3(I),C.sub.4(I+1))pour I.noteq.I.sub.max

"The invention also relates to a computer program comprising code instructions for use of the simulation method according to any one of the above characteristics when it is run on a computer.

"Other advantages and characteristics of the invention will become clear by reading the non-limitative detailed description given below.

BRIEF DESCRIPTION OF THE DRAWINGS

"We will now describe embodiments of the invention by means of non-limitative examples with reference to the appended drawings among which:

"FIG. 1 diagrammatically shows a computer system that can be used to create a fluid flow simulation method, in order to determine at least one aerodynamic coefficient related to an aircraft according to the invention;

"FIG. 2 shows the various steps in a simulation method according to a first embodiment of the invention;

"FIGS. 3A to 3E show the plots according to the different steps in the method in FIG. 2;

"FIG. 4 shows the different steps in a simulation method according to a second embodiment of the invention; and

"FIG. 5 shows the plot according to a step in the method in FIG. 4."

For additional information on this patent application, see: Calmels,

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