Verfahren und Vorrichtung zum numerischen Messen mindestens einer strömungsbezogenen Eigenschaft

Abstract

The invention relates to a method for the numerical measurement of at least one flow-related characteristic of a profile section of a rotating profile body, around which fluid can flow, by means of a numerical flow simulation which is executed on a data-processing system and which calculates a fluid-based flow around the profile section by means of multi-dimensional computational meshes, wherein the method comprises the following steps: providing a numerical flow simulation which can be executed on a data-processing system and which is configured such that the flow velocity of the far field of the numerical flow simulation is set to zero and, instead, a lattice movement of the multi-dimensional computational mesh is performed with a translational velocity in the profile section plane, such that the relative velocity yields the incident-flow velocity of the profile section at a given angle of attack, the symmetry boundary conditions for the edges of the multi-dimensional computational mesh are set to a translationally periodic boundary condition, and the velocity component, resulting from the velocity field of the rotational movement on the edge of the profile section, in the normal direction with respect to the profile section plane are taken into consideration in the inertial terms of the balance equations of the numerical flow simulation, executing the numerical flow simulation as provided above in order to numerically measure and obtain the at least one flow-related characteristic of the profile section.

Claims

1. A method for measurement of at least one flow-related characteristic of a profile section of a rotating profile body, around which fluid can flow, comprising: executing a numerical flow simulation on a data-processing system; and calculating a fluid-based flow around the profile section using one or more multi-dimensional computational meshes, wherein the numerical flow simulation and the data-processing system are configured such that a flow velocity of a far field of the numerical flow simulation is set to zero and, instead, a lattice movement of the one or more multi-dimensional computational meshes is performed with a translational velocity in a profile section plane, such that a relative velocity yields an incident-flow velocity of the profile section of the rotating body at a given angle of attack, symmetry boundary conditions for edges of the one or more multi-dimensional computational meshes are set to a translationally periodic boundary condition, and a velocity component resulting from a velocity field of a rotational movement on an edge of the profile section in a normal direction with respect to the profile section plane are taken into consideration in inertial terms of balance equations of the numerical flow simulation.

2. The method according to claim 1, wherein the at least one flow-related characteristic is an aerodynamic characteristic of the rotating profile body, or a hydrodynamic characteristic of the rotating profile body.

3. The method according to claim 1, wherein the translational velocity of the lattice movement is comprised of a path velocity of the rotational movement at a distance of the profile section plane from an axis of rotation, and a movement in a direction of the axis of rotation.

4. The method according to claim 1 wherein for the numerical flow simulation, a two-dimensional computational mesh is used which is extruded in a normal direction with respect to a computational mesh plane, such that a computational mesh of said one or more multidimensional computational meshes is formed from a layer of three-dimensional elements.

5. The method according to claim 1 wherein along a chord of the profile section consideration is given to a multiplicity of velocity components in the normal direction with respect to the profile section plane which arise from a velocity field over the chord.

6. The method according to claim 1 wherein the calculating step includes calculating from the velocity component in the normal direction with respect to the profile section plane, resulting from the velocity field of the rotational movement on the edge of the profile section, at least one volume-specific inertial force, wherein the at least one volume-specific inertial force is taken into consideration in the inertial terms of the balance equation.

7. The method according to claim 1 wherein a lift coefficient, a resistance coefficient, a moment coefficient, a lift curve, a resistance curve, and a polar and/or a moment curve are numerically measured as flow-related characteristics of the profile section.

8. The method according to claim 1 wherein the rotating profile body around which fluid can flow is a propeller blade, a rotor blade, an impeller blade, a repeller blade, or the blade of a marine propeller.

9. The method according to claim 1 wherein the rotating profile body around which fluid can flow is constituted from a multiplicity of individual profile sections, wherein at least one flow-related characteristic is determined for each individual profile section, and wherein at least one flow-related characteristic of the rotating profile body around which fluid can flow is determined from the respective flow-related characteristics of the individual profile sections.

10. A measuring apparatus for measurement of at least one flow-related characteristic of a profile section of a rotating profile body around which fluid can flow, comprising: a data-processing system on which a numerical flow simulation is executed which calculates a fluid-based flow around the profile section using one or more multi-dimensional computational meshes, wherein the data-processing system and the numerical flow simulation are configured such that a flow velocity of a the far field of the numerical flow simulation is set to zero and, instead, a lattice movement of the one or more multi-dimensional computational meshes is performed with a translational velocity in a profile section plane, such that a relative velocity yields an incident-flow velocity of the profile section at a given angle of attack, symmetry boundary conditions for edges of the one or more multi-dimensional computational meshes are set to a translationally periodic boundary condition, and a velocity component resulting from the velocity field of a rotational movement on an edge of the profile section, in a normal direction with respect to the profile section plane are taken into consideration in inertial terms of balance equations of the numerical flow simulation.

11. The measuring apparatus according to claim 10, wherein the measuring apparatus is configured for carrying out the method according to claim 1.

12. A non-transient computer readable medium encoded with a computer program which, when executed on a data-processing system, performs the method of claim 1.

Description

[0027] The invention will be discussed by way of example on the basis of the appended figures, in which:

[0028] FIG. 1is a schematic illustration of the measuring apparatus according to the invention;

[0029] FIG. 2is a schematic illustration of the velocity field of a profile section of finite extent arranged at an angle of attack, in the projection onto a plane perpendicular to the axis of rotation;

[0030] FIG. 3is a schematic illustration of the components of the mass-specific inertial forces on the edge of the profile section in the section plane, projected onto the chord.

[0031] FIG. 1 shows the measuring apparatus 10, which is in the form of a data-processing system and on which a numerical flow simulation 11 is executed or executable. As input data, the numerical flow simulation of the measuring apparatus 10 firstly receives the shape of the profile section 12 of the profile body to be examined, the radius r.sub.n that describes the distance of the section plane of the profile section from the axis of rotation of the rotating profile body, the angular velocity of the rotation, and the angle of attack of the chord relative to a plane perpendicular to the axis of rotation.

[0032] Furthermore, the numerical flow simulation 11 receives further input data 13 which are intended to become the basis of the numerical flow simulation. These may be for example the incident-flow velocity and the graduation of the angles of attack that are to be examined.

[0033] The numerical flow simulation now calculates, for example, the lift curve of the profile, which constitutes the lift coefficient c.sub.a as a function of the angle of attack of the chord relative to the vector of the incident-flow velocity. For this purpose, the numerical flow simulation is firstly executed for a specific angle of attack , and the flow-related (aerodynamic) coefficients of the chord are determined. The flow-related (aerodynamic) coefficients may for example be the lift coefficient c.sub.a, the resistance coefficient c.sub.w or the moment coefficient c.sub.m. For different angles of attack , these yield the lift curve, the resistance curve and the moment curve.

[0034] For a section plane which rotates at the constant angular velocity at the distance r.sub.n from the axis of rotation, FIG. 2 illustrates the velocity field of the rotational movement of the edge in the projection onto a plane perpendicular to the axis of rotation. The velocity field is temporally constant relative to the section plane. For a vanishing extent s of the profile section in the plane perpendicular to the axis of rotation, the velocity field lies in the section plane and is also spatially constant; it corresponds to a translational movement of the edge with the vector v.sub.t of the path velocity on the circular path at the distance r.sub.n from the axis of rotation.

[0035] For a finite extent s of the profile in the plane perpendicular to the axis of rotation, the velocity field of the translational movement with the path velocity v.sub.t has superposed on it a temporally constant velocity field which is perpendicular to the profile plane and which increases linearly with the distance r.sub.t to the plane perpendicular to the profile plane through the axis of rotation. For the calculation of the lift and resistance curve of the profile without taking into consideration the influence of the rotation, the extent s of the profile section in the plane perpendicular to the axis of rotation is disregarded, and the lift and resistance curves are calculated with a parallel incident flow, the velocity of which corresponds to the oppositely oriented path velocity v.sub.t in the section plane, which can be supplemented by a corresponding component in the case of a forward movement in the direction of the axis of rotation.

[0036] To obtain a numerical method for taking into consideration the influence of the rotation, a formulation of the balance equations of the model of continuum mechanics for rotating computational meshes is used, which was developed in Kroll, N.: Berechnung von Strmungsfeldern um Propeller und Rotoren im Schwebeflug durch die Lsung der Euler-Gleichungen [Calculation of flow fields around propellers and rotors in hovering flight by solving the Euler equations], Dissertation, Faculty of Mechanical Engineering and Electrical Engineering at the Carolo-Wilhelmina Technical University of Braunschweig, 1989, and which is used in the numerical flow solver Tau in order to calculate three-dimensional flows around rotating profile bodies. In this formulation, the flow velocity v in the inertial system is not divided into a relative velocity with respect to a rotating reference system and a velocity of the rotating reference system with respect to the inertial system, but instead, the change in the flow velocity of the inertial system with respect to a rotating reference system is considered. Normally, a position vector r in the inertial system is broken down into the position vector r.sub.0 with respect to the origin of the rotating reference system and the position vector r.sub.r from the origin to a point of the rotating reference system that performs a rotational movement, the change in position of which at a time t.sub.0 is described by the transformation matrix T

r=r.sub.0+Tr.sub.r.

[0037] Deriving this relationship with respect to time, one obtains the relative velocities

[00001]$\frac{r}{t}=\frac{r_0}{t}+\underset{\underset{}{}}{\frac{T}{t}}.Math.r_r+\underset{\underset{I}{}}{T}.Math.\frac{r_r}{t}.$

[0038] In the balance equations, the derivation is considered at the respectively present point in time t.sub.0=O, at which a change in position does not yet occur owing to the rotation. In this case, the transformation matrix T for the rotation is identical to the unit matrix I, and the matrix vector product with the derivative with respect to time of the transformation matrix T for the rotation can be represented as a cross product with the vector of the angular velocity . By means of a further derivation of this relationship with respect to time t, one obtains the centripetal and the Coriolis acceleration, which relate to the position vector r.sub.r and the velocity v.sub.r=dr.sub.r/dt in the rotating reference system. In the alternative formulation, the division of the flow velocity v in the inertial system is omitted, and only the change thereof with respect to time with respect to the rotating reference system is considered. Inserting the velocity vector v into the relationship of the above-stated formula, one obtains

[00002]$\frac{v}{t}=\underset{\underset{}{}}{\frac{T}{t}}.Math.v+\underset{\underset{I}{}}{T}.Math.\frac{v}{t}.$

[0039] such that the relative acceleration v is obtained as the only additional term. The product of the relative acceleration v with the density arises, in the derivative with respect to time of the volume integral, on the left-hand side of the momentum equation, which, as a vectorial equation, comprises three scaler equations for the three spatial directions. If this term is moved to the right-hand side of the momentum equations, it can be interpreted, with a negative sign, as a volume-specific inertial force.

[0040] If a profile moves through an inviscid flow which is at rest relative to the inertial system, the additional acceleration term v is equal to zero, and the rotation has no influence if the flow velocity owing to the displacement is disregarded.

[0041] A mass-specific inertial force in the rotating reference system is equal to the negative relative acceleration v. FIG. 3 shows the section plane of the profile section and the projection of the axis of rotation onto the section plane. The mass-specific inertial forces that act on the edge of the profile section are illustrated in FIG. 3 in the projection onto the chord. The mass-specific inertial forces vanish at the points of intersection of the edge with the plane perpendicular to the section plane through the axis of rotation, and increase linearly with the distance r.sub.t to said plane. Decelerating mass-specific inertial forces arise in front of said plane, and accelerating mass-specific inertial forces arise behind said plane. The mass-specific inertial forces have the angle of attack relative to the chord, which is identical to the angle of attack of the chord relative to a plane perpendicular to the axis of rotation.

[0042] The mass-specific inertial forces act in the section plane in the boundary layer of the flow. The boundary layer of the flow constitutes a thin layer in the vicinity of the edge of the profile section, in which viscous forces play a role. The inertial forces in the section plane arise owing to the velocity field of the rotational movement of the edge in a normal direction with respect to the section plane, which propagates into the flow field of the boundary layer owing to viscous forces. In FIG. 3, the normal components of the flow velocity are illustrated in the projection of the mass-specific inertial forces of the edge onto the chord. A cross corresponding to the fin of an arrow indicates that the velocity components are directed away from the viewer normally with respect to the profile plane; a dot corresponding to an arrow tip shows that the velocity components are directed towards the viewer normally with respect to the profile plane. The plane of the drawing corresponds to the section plane.

[0043] The inertial terms that have hitherto been used for the calculation of a three-dimensional flow around a rotating profile body using a rotating computational mesh are used for the calculation of a planar flow around a profile section using a non-rotating two-dimensional extruded computational mesh. The inertial forces in the section plane that arise from the velocity field normal to the section plane, as shown in FIG. 3, are responsible for a correct representation of the influence of the rotation and the resulting flow-related characteristics. The inertial forces have, in the rear part of the profile section, a component in the flow direction, which component counteracts the deceleration of the boundary layer owing to the pressure increase and thus prevents a premature detachment of the flow. In the front part of the profile section, the inertial forces have a component counter to the flow direction, which component counteracts the acceleration of the boundary layer owing to the displacement of the flow, and the associated pressure drop. Since the flow is intensely accelerated in this region, the components counter to the flow direction do not lead to a detachment of the flow. By taking into consideration the inertial forces of a three-dimensional flow field in the calculation of a planar flow around a profile, in which velocity components are present in all spatial directions, secondary effects of the inertial forces in the boundary layer are also taken into consideration.

LIST OF REFERENCE DESIGNATIONS

[0044] 10 Measuring apparatus

[0045] 11 Numerical flow simulation

[0046] 12 Profile section

[0047] 13 Input data

[0048] 14 Plane perpendicular to the axis of rotation

[0049] 15 Chord