JP7074001B2 - Analyst - Google Patents

Description

The present invention relates to an analyzer that analyzes the relationship between a flow field around a moving structure (eg, flow velocity, vorticity, etc.) and wind noise reaching the inside of the structure.

Techniques for analyzing sounds generated during the movement of structures such as vehicles have been developed. For example, a conventional device acquires the "amplitude of pressure fluctuation" and the "average flow velocity" at an arbitrary position on the surface of the vehicle model by a simulation of running the vehicle model, and radiates from the surface of the vehicle model based on these values. The sound power, which is the total energy of the sound to be produced, is calculated (see, for example, Patent Document 1).

Japanese Unexamined Patent Publication No. 2017-06727

By the way, while the structure (for example, a vehicle) is moving, the noise generated by the flow of the fluid around the structure reaches the inside of the structure. In the present specification, the noise that reaches the inside of the structure in this way is referred to as "wind noise". Wind noise changes under the influence of the flow field around the structure. Therefore, in order to reduce the wind noise, it is specified which part (position) of the flow field around the structure has a strong influence on the wind noise, and the flow field of the relevant part is changed. (That is, it is necessary to change the shape of the parts of the structure). However, there is no unified method for "the method of identifying the part of the flow field that greatly contributes to the wind noise", and in reality, the engineer is based on his own know-how and knowledge. The part of is specified. For this reason, there is a problem that the examination results vary depending on the engineer and a lot of trial and error occurs.

The present invention has been made to solve the above problems, and one of the objects thereof is a flow field around a structure such as a vehicle and a wind noise reaching the inside of the structure. It is an object of the present invention to provide a technique capable of appropriately identifying the position of a flow field around a structure, which greatly contributes to wind noise, by analyzing the relationship between the two.

The analysis device of the present invention (hereinafter, may be referred to as "the device of the present invention") is an analysis device (10) that analyzes wind noise generated in a moving structure.
The analyzer is
The unsteady CFD calculation process for moving the structure model (20) that models the structure is executed, and the flow field in the predetermined region (21) of the flow fields around the structure model (20) is executed. The average flow velocity (U-) and average vortex (Ω-) at a predetermined time are calculated for each spatial node (z) which is a node in the predetermined region (21), and the angle to be analyzed for wind noise. In the angular frequency band of interest ([θ _l , θ _h ]), which is a frequency band, a value based on the amplitude (u to _θ ) of the turbulence flow velocity in the predetermined region (21) is calculated for each spatial node (z). First calculation means (11, step 605, step 610, step 615) and
The structure is based on the average flow velocity (U−) calculated by the first calculation means, the average vorticity (Ω−), and the value based on the amplitude (u to _θ ) of the turbulence flow velocity. The first index (IDS) indicating the contribution of the flow field at the spatial node (z) to the sound intensity (Iin _n ) incident along the normal direction at the observation point (x) on the analysis surface in the above is calculated. The second calculation means (11, step 620) and
Based on the first index calculated by the second calculation means, the acoustic power (Pin) reaching the analysis surface is calculated, and at the spatial node (z) with respect to the sound power reaching the analysis surface. A third calculation means (11, step 630) for calculating a second index (APwDS) indicating the contribution of the flow field, and
Display means (13, 19, step 640) for displaying information regarding the distribution of the size of the second index in the predetermined region, and
To prepare for.

According to the apparatus of the present invention, information regarding the size distribution of the second index indicating the contribution of the flow field at the spatial node (z) to the sound power reaching the analysis surface is displayed by the display means. Therefore, the user can appropriately identify the position of the flow field around the structure, which greatly contributes to the wind noise reaching the inside of the structure.

In the above description, in order to help understanding of the invention, the reference numerals used in the embodiments are attached in parentheses to the configurations of the invention corresponding to the embodiments, but the constituent elements of the invention are the above-mentioned reference numerals. It is not limited to the embodiment defined by.

It is a block diagram which shows the structure of the analysis apparatus which concerns on embodiment of this invention (hereinafter, referred to as "the present-implementing apparatus"). It is a schematic diagram of the vehicle model and the flow domain which is the object of the unsteady CFD simulation. It is a figure explaining the acoustic intensity used as an index at the time of analyzing the wind noise (in-vehicle sound) in this implementation device. It is a figure used to explain the derivation method of the APDS calculation formula, and is a schematic diagram of a rigid body model and a flow domain. It is a schematic diagram of a rigid body model and a flow domain. It is a flowchart which showed the "analysis routine" which the CPU of this execution apparatus executes. It is a distribution map of the sound intensity on the analysis surface (left front side glass) of a vehicle model. This is an example of the isosurface distribution of APwDS displayed as an image on the display screen based on the first reference value of APwDS. This is an example of the isosurface distribution of APwDS displayed as an image on the display screen based on the second reference value of APwDS. It is a figure for demonstrating the plane (evaluation cross section) in which the distribution map of the parameter constituting an IDS is created. It is a distribution map of the average flow velocity around the left side mirror in the evaluation cross section (see the broken line L in FIG. 10). It is a distribution map of the turbulence flow velocity around the left side mirror in the evaluation cross section (see the broken line L in FIG. 10). (A) is a "distribution map of sound intensity on the analysis surface (left front side glass)" when the analysis process is executed for the first vehicle model using the present implementation device, and (b) is the present. It is a "distribution map of the sound intensity on the analysis surface (left front side glass)" when the analysis process is executed for the 2nd vehicle model using the executing apparatus. "Difference in measured in-vehicle sound between the first vehicle and the second vehicle", "Sound power calculated by analyzing the first vehicle model using the present implementation device, and the implementation device. It is a graph which showed "the difference from the acoustic power calculated by analyzing the 2nd vehicle model".

<Configuration of this implementation device>
The present embodiment analyzes wind noise generated when various structures move, but in the present embodiment, a vehicle among the structures will be described as an example.

As shown in FIG. 1, the analysis device 10 includes a calculation unit 11, an input unit 12, and an output unit 13. The arithmetic unit 11 includes a CPU 14, a RAM 15, a ROM 16, a hard disk (HDD) 17, and an I / O interface 18.

In the ROM 16 and / or HDD 17, the data of the three-dimensional model of the vehicle to be analyzed for wind noise, the data of the flow domain showing the analysis range, and the data necessary for the unsteady CFD (computational fluid dynamics) simulation. Etc. are stored in advance.

Further, the ROM 16 stores instructions (programs, routines) executed by the CPU 14. The CPU 14 is adapted to realize various functions described below by executing the instruction.

The arithmetic unit 11 is connected to the input unit 12 and the output unit 13 via the I / O interface 18. The input unit 12 is a device that receives various requests from the user, and includes a keyboard and a mouse. Therefore, the user can specify the reference value, the parameter, and the like of the index (APwDS described later) by using the input unit 12. The output unit 13 has a display screen 19 that can be visually recognized by the user.

<Vehicle model configuration>
FIG. 2 is a diagram schematically showing a three-dimensional model 20 of a vehicle (hereinafter, simply referred to as “vehicle model 20”) and a flow domain 21. The vehicle model 20 corresponds to an example of a "structure model". As shown in FIG. 2, the spatial coordinate system of the vehicle model 20 includes an e1 axis (vehicle front-rear direction), an e2 axis (vehicle width direction), and an e3 axis (height direction). In addition, the origin is set at a position separated from the reference point (for example, the center of gravity) of the vehicle model 20 by a predetermined distance (including a zero value) in a predetermined direction.

The flow domain 21 is a region in the space around the vehicle model 20 that indicates the range in which the unsteady CFD calculation is performed. The flow domain 21 includes "a flow field of a portion of the flow field around the vehicle model 20 that may affect the sound intensity (described later) incident on the surface of the left front side glass 22 in the normal direction. It is set as "the area". Specifically, in the flow domain 21, a portion overlapping with the vehicle model 20 is hollowed out from a space having a substantially rectangular parallelepiped shape including the left front side glass 22, the left side mirror 23, the left front pillar, the left half of the front glass, and the like. Has a shape. The flow domain 21 can be freely set depending on which part of the vehicle model 20 is to be analyzed. The flow domain 21 corresponds to an example of a “predetermined area”.

<Analysis of wind noise>
In the following, a specific method for analyzing the wind noise generated when the vehicle is running will be described. Hereinafter, the wind noise (noise reaching the inside of the vehicle) is referred to as "in-vehicle sound P _out " (see FIG. 3).

(Relationship between the sound inside the vehicle and the acoustic power that reaches the surface of the vehicle)
As shown _in the following equation (1), the vehicle interior sound P _out is determined by the sound power Pin reaching the vehicle surface and the vehicle surface transmission loss TL. The vehicle surface transmission loss TL depends on the material properties of the vehicle surface. The vehicle surface transmission loss TL can be determined in advance by measurement.

Here, _in order to analyze the relationship between the sound _inside the vehicle and the flow field around the vehicle, a relational expression expressing the relationship between the sound power Pin and the flow field around the vehicle is constructed.

The sound power _pin can be expressed by the following equations (2) and (3). Therefore, the sound power _Pin can be calculated using the sound pressure on the vehicle surface (hereinafter, may be simply referred to as “surface sound pressure”).

The symbols in the equation (2) and the equation (3) are as follows.

The surface sound pressure pa can be evaluated by the "APDS (Acoustic Pressure Density Source)" described later. APDS is an index that quantitatively indicates the relationship between the flow field around the vehicle and the fluctuation of the surface sound pressure (in other words, the "flow field (state) at any position around the vehicle" is "arbitrary on the vehicle surface". It is an index showing how much it contributes to the fluctuation of the surface sound pressure at the position of. The APDS has physical quantities such as an average flow velocity (U- described later), a turbulence flow velocity (u- _θ described later), and an average vorticity (Ω- described later) of the flow field at an arbitrary position around the vehicle as parameters.

In addition, the "fluctuation of surface sound pressure at an arbitrary position on the vehicle surface" can be calculated (predicted) based on the value obtained by spatially integrating the APDS in the flow field in the predetermined region (flow domain 21) around the vehicle. can. Therefore, this implementation device calculates the average flow velocity, turbulence flow velocity, and average vorticity of the flow field for each position in the flow domain 21 by unsteady CFD calculation processing, and based on these values, APDS is calculated in the flow domain. Calculated for each position within 21.

More specifically, the unsteady CFD calculation process calculates an autocorrelation function of turbulence flow velocity (strictly speaking, the amplitude of the turbulence flow velocity) u to _θ for each frequency (angular frequency) (θ: angular frequency. θ). = 2πf). The "autocorrelation function of the amplitude u to _θ of the turbulence flow velocity" corresponds to an example of the "value based on the amplitude of the turbulence flow velocity".

The autocorrelation function is calculated in the frequency band to be analyzed for wind noise (hereinafter, the frequency band is also referred to as "the frequency band of interest"). The frequency band of interest can be selected by the user, and for example, a frequency band having a center frequency _fm of 500 Hz, 1 kHz, 2 kHz, or 4 kHz can be selected. Typically, a frequency band of 2 kHz or higher can be selected. For example, when 2 kHz (lower limit frequency f _l = 1420 Hz, upper limit frequency f _h = 2840 Hz) is selected as the frequency band of interest, the autocorrelation function of the turbulence flow velocity is the position within the flow domain 21 within the range of 1420 Hz to 2840 Hz. Calculated for each.

ここで、上記式（４）中のθ_ｌ及びθ_ｈは、着目角周波数帯の下限角周波数及び上限角周波数をそれぞれ表し、Ｆ_θ ^＊は、関数Ｆ_θの複素共役を表す。即ち、本明細書では、自己相関関数は、「任意の関数Ｆ_θとその複素共役関数Ｆ_θ ^＊との積（後述）を着目角周波数帯において積分した値」として定義される。 The autocorrelation function of any function F _θ is defined by the following equation (4).

Here, θ _l and θ _h in the above equation (4) represent the lower limit angular frequency and the upper limit angular frequency of the angular frequency band of interest, respectively, and F _θ ^* represents the complex conjugate of the function F _θ . That is, in the present specification, the autocorrelation function is defined as "a value obtained by integrating the product (described later) of an arbitrary function F _θ and its complex conjugate function F _θ ^* in the angular frequency band of interest".

The surface of the left front side glass 22 of the vehicle model 20 is defined as an "analyzed surface". Further, the i-th node x counted from any reference node on the analysis surface is defined as _xi (i: 1 to m), and the j-th spatial node counted from any reference space node in the flow domain 21 is defined. z is defined as z _j (j: 1 to n). The APDS for the kth node _{x k} (k: 1 to m) is calculated at the total space node zj in the flow domain 21, respectively.

Here, the value obtained by spatially integrating the APDS in the frequency band of interest for the node x _k at the entire spatial node z _j in the flow domain 21 is “the surface sound pressure fluctuation pa _θ (x _k ) of the frequency band of interest at the node x _k ). It is an approximate value of "autocorrelation function of" (described later). Therefore, the value of APDS of the frequency band of interest at each spatial node zj is the autocorrelation function of the surface sound pressure fluctuation pa _θ ( _{x k} ) of the frequency band of interest at the node x _k per unit volume of the flow domain 21. It can be interpreted as representing an approximate value of. In the following, when it is not necessary to distinguish a certain node x _k from another node x _i , the notation of "k" and "i" is omitted. The same applies to the spatial node _zi .

(Derivation of APDS calculation formula)
Next, the APDS calculation formula and the method for deriving the calculation formula will be described. Hereinafter, the amplitude of pressure fluctuation, the amplitude of sound pressure fluctuation, and the amplitude of fluid flow pressure fluctuation on the surface of the structure are referred to as "surface pressure fluctuation", "surface sound pressure fluctuation", and "surface fluid flow pressure fluctuation", respectively. .. Further, the node x is referred to as an "observation point x", and the spatial node z is referred to as an "evaluation point z".

APDS is a relational expression between the surface pressure fluctuation (that is, the sum of the surface sound pressure fluctuation and the surface fluid flow pressure fluctuation) in the rigid body model calculated based on the known Powell equation and the flow field around it. Is defined based on the formula converted from the time domain to the frequency domain. However, the Powell formula is expressed in a format suitable for deriving the APDS calculation formula. Therefore, in the following, the rigid body model and the flow domain will be described first with reference to FIG. 4, and then the derivation of the Powell formula suitable for the derivation of the APDS calculation formula will be described. Next, the derivation of the relational expression between the surface pressure fluctuation and the flow field in the time domain will be described, and then the derivation of the APDS calculation formula will be described.

1. 1. Rigid body model and flow domain FIG. 4 shows a schematic diagram of the rigid body model 41 and the flow domain 42. The rigid body model 41 (hereinafter, also simply referred to as “rigid body 41”) has an observation point x on its surface S. The flow domain 42 is a flow field of a portion of the flow field around the rigid body 41 that may affect the surface pressure fluctuation at the observation point x. The flow domain 42 has a plurality of evaluation points z inside thereof. APDS (x, z) is an index showing the contribution of the flow field at the evaluation point z to the surface sound pressure fluctuation at the observation point x. The other characters in FIG. 4 will be described later.

ここで、ρは流れ場の密度であり、ｕは流れ場の流速（ベクトル量）であり、Ｄ／Ｄｔは物質微分であり、ｐは剛体４１の表面における圧力（圧力変動、表面圧力変動）であり、ηは流れ場の粘性係数である。 2. 2. Derivation of Powell equation The following equation (5) shows the Navier-Stokes equation when the body force is zero.

Here, ρ is the density of the flow field, u is the flow velocity (vector amount) of the flow field, D / Dt is the material derivative, and p is the pressure (pressure fluctuation, surface pressure fluctuation) on the surface of the rigid body 41. And η is the viscosity coefficient of the flow field.

を用いて式変形すると、下記式（６）が得られる。なお、上記の関係式中のＡは任意のベクトルを表す。

ここで、νは流れ場の動粘性係数であり、ν＝η／ρである。 The material derivative of the above equation (5) is rewritten using the partial derivative, and then the following relational expression;

By transforming the equation using, the following equation (6) is obtained. In addition, A in the above relational expression represents an arbitrary vector.

Here, ν is the kinematic viscosity coefficient of the flow field, and ν = η / ρ.

を用いて式変形すると、下記式（７）が得られる。なお、ωは流れ場の渦度（ベクトル量）であり、Ｂはエンタルピーである。

Subsequently, the above equation (6) is changed to the following relational equation;

By transforming the equation using, the following equation (7) is obtained. Note that ω is the vorticity (vector quantity) of the flow field, and B is the enthalpy.

が成立するため、上記式（７）は下記式（８）によって近似できる。

The flow field of this embodiment is an incompressible fluid or a microcompressible fluid, but in this case, the following relational expression;

Therefore, the above equation (7) can be approximated by the following equation (8).

なお、上記式（９）中の「×」は乗算記号を表す。本明細書では基本的に乗算記号は省略して記載するが、明示したほうが理解し易い場合は例外的に記載する。 By multiplying both sides of the above equation (8) by the density ρ of the flow field and taking the divergence, the following equation (9) is obtained.

The "x" in the above equation (9) represents a multiplication symbol. In this specification, the multiplication symbol is basically omitted, but if it is easier to understand, it is described as an exception.

「流れ場の密度ρ」と「流れ場の流速ｕの時間についての偏微分」との積の発散（即ち、下記式（１１）の左辺）を上記式（１０）を用いて式変形すると、下記式（１１）の右辺のようになる。

ここで、ｃは流れ場の音速である。表面圧力変動ｐ、流れ場の密度ρ、及び、流れ場の音速ｃの間には以下の関係が成立する。

Here, the relational expression shown in the following equation (10) is established between the flow velocity u of the flow field and the density ρ of the flow field.

When the divergence of the product of "the density ρ of the flow field" and "the partial differential with respect to the time of the flow velocity u of the flow field" (that is, the left side of the following equation (11)) is transformed by the above equation (10), It is as shown on the right side of the following equation (11).

Here, c is the speed of sound in the flow field. The following relationship holds between the surface pressure fluctuation p, the density ρ of the flow field, and the speed of sound c of the flow field.

が成立する。なお、レイノルズ数Ｒｅは、Ｒｅ＝ｕＬ／νとして定義され、Ｌは流れ場の代表長さを表す。上記式（１１）の右辺の括弧内の項を以下に示すように式変形して上記関係式を適用すると、式（１１）の右辺の括弧内の項は下記式（１２）によって近似される。

By the way, the flow field of the present embodiment is a high Reynolds number flow (that is, a flow having a relatively large flow velocity, for example, 100 km / h to 140 km / h). In the high Reynolds number flow, the following relational expression;

Is established. The Reynolds number Re is defined as Re = uL / ν, where L represents the representative length of the flow field. When the term in parentheses on the right side of the above equation (11) is transformed as shown below and the above relational expression is applied, the term in parentheses on the right side of the equation (11) is approximated by the following equation (12). ..

When the above equation (9) is modified (approximate) using the above equations (11) and (12), the following equation (13) is obtained.

が成立するため、上記式（１３）をこれらの関係式を用いて式変形すると、下記式（１４）に示すパウエル式が得られる。なお、上記の関係式のｃ_０は静止状態のときの流れ場の音速であり、ρ_０は静止状態のときの流れ場の密度である。

Here, the flow field of the present embodiment is a low Mach number flow (that is, a flow field in which the ratio of the flow velocity of the fluid to the speed of sound is relatively low). In the low Mach number flow, the following relational expression;

Is satisfied. Therefore, by transforming the above equation (13) using these relational equations, the Powell equation shown in the following equation (14) can be obtained. In the above relational expression, c ₀ is the speed of sound of the flow field in the stationary state, and ρ ₀ is the density of the flow field in the stationary state.

ここで、観測点ｘ及び評価点ｚは上述したとおりであり（図４参照）、τは過去の時刻である。なお、δ（ｘ）はディラックデルタ関数である。加えて、上記式（１５）中のグリーン関数Ｇは、自由空間においては下記式（１６）のように表される。

3. 3. Derivation of the relational expression between the surface pressure fluctuation and the flow field in the time domain The Green's function G satisfies the relational expression of the following equation (15).

Here, the observation point x and the evaluation point z are as described above (see FIG. 4), and τ is a past time. Note that δ (x) is a Dirac delta function. In addition, the Green's function G in the above equation (15) is expressed as the following equation (16) in free space.

Ｈ（ｚ）はヘビサイド関数（Heaviside Unit Function）であり、下記式（１８）によって定義される。

ここで、図４に示すように、Ｖはフロードメイン４２を表すかたまりであり、Ｓ＋は剛体４１の表面Ｓを取り囲む仮想表面である。上記式（１８）中の「z in V」とは、評価点ｚがフロードメイン４２の内部に位置している場合を示し、「z inside S+」とは、評価点ｚが仮想表面Ｓ＋の内部に位置している場合を示す。 Considering the object boundary conditions, the Powell equation shown in the above equation (14) is expressed as the following equation (17).

H (z) is a Heaviside Unit Function and is defined by the following equation (18).

Here, as shown in FIG. 4, V is a mass representing the flow domain 42, and S + is a virtual surface surrounding the surface S of the rigid body 41. “Z in V” in the above equation (18) indicates a case where the evaluation point z is located inside the flow domain 42, and “z inside S +” means that the evaluation point z is inside the virtual surface S +. Indicates the case where it is located in.

ここで、式中の（・）は任意の値との内積を表す。加えて、図４に示すように、剛体４１は、その表面Ｓのうち観測点ｘとは異なる位置に評価点ｙを有する。式中のｎは、当該評価点ｙの法線ベクトルｎ（ｙ）を表し、ｄＳは、評価点ｙ近傍の表面面積ｄＳ（ｙ）を表す。 This Heaviside function H (z) satisfies the integral equation of the following equation (19).

Here, (・) in the formula represents an inner product with an arbitrary value. In addition, as shown in FIG. 4, the rigid body 41 has an evaluation point y at a position different from the observation point x on the surface S thereof. In the formula, n represents the normal vector n (y) of the evaluation point y, and dS represents the surface area dS (y) in the vicinity of the evaluation point y.

The one item, two items, and the right side of the left side of the above equation (17) can be transformed as the following equations (17-1), (17-2), and (17-3), respectively.

By substituting the above equations (17-1) to (17-3) into the above equation (17), the following equation (20) is obtained.

The two items on the right side of the above equation (20) (-signs are omitted) can be transformed as in the following equation (20-1).

By substituting the above equation (20-1) into the above equation (20), the following equation (21) is obtained.

When the above equation (16) is used, the integral display of the above equation (21) becomes as shown in the following equation (22).

When one item on the right side of the above equation (22) is expanded using the above equation (21), the following equation (22-1) is obtained. In the following, for convenience of notation, when describing the equation modification of each term on the right side of the equation (22), the time integral is omitted.

By expanding the two items and three items on the right side of the above equation (22) using the above equation (21), the following equation (22-2) is obtained.

The four items on the right side of the above equation (22) can be transformed as shown in the following equation (22-3).

By substituting the above equations (22-1) to (22-3) into the above equation (22), the following equation (23) is obtained.

When the virtual surface S + is converged on the surface S of the rigid body 41, the above equation (23) can be rewritten as the following equation (24).

Here, in the high Reynolds number flow, the three items on the right side of the above equation (24) are so small that they can be ignored with respect to the four items. In addition, when the rigid body 41 is stationary, there is no flow velocity, so the two items on the right side are equal to zero. Therefore, the above equation (24) can be simplified as the following equation (25).

Since there is no flow velocity on the surface of a stationary object, the enthalpy B is expressed by the following equation.

By defining the right-hand side p / ρ of the above equation as p / ρ = p _* and substituting the enthalpy B into the above equation (25), the relational expression of the following equation (26) is obtained. This relational expression is "the relational expression between the surface pressure fluctuation and the flow field in the time domain".

4. Derivation of APDS calculation formula Since the relational formula of the above formula (26) includes the value (function) p _* (= p / ρ) based on the surface pressure fluctuation p on both sides, the surface pressure fluctuation p at the observation point x is the flow velocity. It cannot be calculated directly from u and vortex degree ω. Therefore, in the following, the term including p _* is deleted from the right side by the transformation of the equation, and the relational expression between "surface pressure fluctuation p at the observation point x" and "flow velocity u of the flow field and vorticity ω" is derived.

As shown in FIG. 5, the region near the observation point x on the surface S of the rigid body 41 is defined as the surface region Sx, and the normal vector of the surface region Sx is n (x). The surface region Sx is a sufficiently large plane. In addition, two points x + and x− having the same distance from the observation point x are defined on the normal vector n (x). The point x + is located outside the rigid body 41, and the point x− is located inside the rigid body 41. Other characters will be described later. By substituting the points x + and x- into the above equation (25) as observation points, the following equations (25-1) and (25-2) are obtained.

The following equation (27) is obtained by adding both sides of equations (25-1) and (25-2) and taking the limit when approaching x for x- and x +, respectively. In the following equation modification, H (x +) = 1 and H (x−) = 0 are used (see equation (18)).

The items 1 and 2 on the right side of the above equation (27) can be transformed into the following equations (27-1) and (27-2), respectively. Note that S \ Sx in the equation represents a portion of the surface S of the rigid body 41 that does not include the surface region Sx (see FIG. 5).

By substituting the above equations (27-1) and (27-2) into the above equation (27), the following equation (28) is obtained.

ここで、式中のＡ_θ（ｘ）は角周波数θにおける関数Ａ（ｘ，ｔ）の大きさ（振幅）を表す。Ａ_θ（ｘ）は複素数であり、その複素共役Ａ_θ ^＊（ｘ）は下記（２９）の関係式を満たす。

The Fourier transform is defined by the following equation.

Here, A _θ (x) in the equation represents the magnitude (amplitude) of the function A (x, t) at the angular frequency θ. A _θ (x) is a complex number, and its complex conjugate A _θ ^* (x) satisfies the relational expression (29) below.

When the Fourier transform is applied to the above equation (27) and the Fourier transform result of the convolution integral is used, the following equation (30) is obtained.

ここで、ｋ_０は角周波数θ成分の波数（いわゆる音響波数）であり、ｋ_０＝θ／ｃ_０である。ｒは観測点ｘと評価点ｚとの距離である。 Here, G _θ (x, z) obtained by Fourier transforming the Green's function G is expressed by the following equation (31) and satisfies the relational equation (so-called Helmholtz equation) of the following equation (32).

Here, k ₀ is the wave number of the angular frequency θ component (so-called acoustic wave number), and k ₀ = θ / c ₀ . r is the distance between the observation point x and the evaluation point z.

The gradient of G _θ (x, z) can be expressed by the following equation (33) using the above equation (31). The vector r in the equation is a vector from the observation point x to the evaluation point z.

Here, the pressure generated on the surface of the rigid body 41 is composed of the fluid flow pressure fluctuation and the sound pressure. Since the fluid flow pressure fluctuation moves at the fluid flow velocity and does not propagate to a long distance, the acoustic compact condition (k ₀ r << 1) is satisfied. Therefore, the portion of the gradient of G _θ (x, z) in the above equation (33) that contributes to the surface fluid flow pressure fluctuation depends on the angular frequency θ as expressed by the following equation (33-1). It can be approximated only by the function of the distance r.

On the other hand, since the sound pressure moves at the speed of sound and propagates to a distant place, the acoustic compact condition is not satisfied (that is, (k ₀ r >> 1) at a distant point). Therefore, the portion of the gradient of G _θ (x, z) in the above equation (33) that contributes to the surface sound pressure fluctuation is expressed by the following equation (33-2).

The autocorrelation function (see the above equation (4)) of the "function p _{* θ} (x) based on the surface pressure fluctuation p _θ (x) at the observation point x" on the left side of the above equation (30) is the following equation (34). ).

The above equation (34) is expressed as the following equation (35) using the acoustic compact condition of the gradient of G _θ (x, z) (see equation (33)).

Here, the correlation distance l _{x, cr} , the correlation area S _{x, cr} (see FIG. 5) and the correlation volume V _{x, cr} of the physical quantity of any observation point x in the angular frequency band of interest [θ _l , θ _h ] are set, respectively. It is defined by the following equations (36-1), (36-2) and (36-3). Note that θ _m in the equation is the central angle frequency of the angular frequency band of interest (θ _m = 2πf _m ).

That is, the correlation area S _{x, cr} is proportional to the square of the average flow velocity, and the correlation volume V _{x, cr} is proportional to the cube of the average flow velocity.

Since the angular frequency band of interest in this embodiment is relatively large, the correlation distances l _{x and cr} are relatively small. Therefore, the correlation area S _{x, cr} and the correlation volume V _{x, cr} are also relatively small. Therefore, as shown in FIG. 5, the correlation area S _{x, cr} is included in the surface region S x (S _{x, cr} ⊂ Sx). Here, the integrand of one item on the right side of the above equation (35) includes the evaluation point y on the surface S of the rigid body 41, and the region (S \ Sx) of the surface S that does not include the surface region Sx. ) Is integrated. Therefore, the physical quantity of the observation point x has no correlation with the physical quantity of the evaluation point y, and as a result, one item on the right side of the above equation (35) becomes equal to zero.

即ち、自己相関関数（式（４）参照）は、任意の関数Ｆ_θのノルムを着目角周波数帯において積分した値である。 In addition, in the following, the product of an arbitrary function F _θ and its complex conjugate function F _θ ^* is referred to as a “norm of the function F _θ ” and is defined as in the following equation (37).

That is, the autocorrelation function (see equation (4)) is a value obtained by integrating the norm of an arbitrary function F _θ in the angular frequency band of interest.

Thereby, the above equation (35) can be expressed as the following equation (38).

This autocorrelation function can be transformed as shown in the following equation (39).

Here, z1 and z2 in the equation are arbitrary evaluation points in the flow domain 42, and z1 ≠ z2. The correlation between the physical quantity of the evaluation point z1 and the physical quantity of the evaluation point z2 in the angular frequency band of interest can be ignored when the evaluation point z1 is not included in the correlation volume V _{z2, cr} of the evaluation point z2. Therefore, the above equation (39) can be further modified as the following equation (40).

Of the "part integrated for the angular frequency band of interest" on the right side of the above equation (40), the portion that contributes to the surface sound pressure fluctuation is approximated as in the following equation (41) using the above equation (33-2). can.

As shown in the following equations (42-1) and (42-2), the flow velocity u of the above equation (41) can be decomposed into an average flow velocity U- as an average component and a turbulence flow velocity u-as a turbulence component. The vorticity ω can be decomposed into an average vorticity Ω− as an average component and a turbulence vorticity ω or more as a turbulence component. In addition, "-" of "U-" and "Ω-" is a notation representing an average, and is a substitute for the bar attached above the letters U and Ω in the formula described later. The "-" in "u-" is a notation representing a turbulence component when the flow velocity u is averaged, and is a substitute for the tilde attached above the letter u in the formula described later. The "~" in "ω ~" is a notation representing the turbulence component when the vorticity ω is averaged, and is a substitute for the tilde attached above the character ω in the formula described later.

ここで、ｒ１、ｒ２及びｒ３は、観測点ｘを原点としたときのベクトルｒのｅ１成分、ｅ２成分及びｅ３成分である。 In addition, in the spatial coordinate system of the rigid body 41, the vector r is defined by the following equation (43).

Here, r1, r2, and r3 are the e1 component, the e2 component, and the e3 component of the vector r when the observation point x is the origin.

By substituting these equations (42-1), (42-2) and (43) into the right-hand side of the above equation (41), the right-hand side can be transformed into the following equation (44). Since the product of the turbulent components is so small that it can be ignored, the description is omitted in the following equation (44).

Here, the correlation function of two arbitrary functions E _θ and the function F _θ is defined as the following equation (45) in the angular frequency band of interest.

ここで、ｋは流速ｕ_θと渦度ω_θとの関係を規定した定数である。 Using the above equations (4) and (45), the relational expressions shown in the following equations (46-1) to (46-6) can be obtained from the vortex uniform isotropic hypothesis.

Here, k is a constant that defines the relationship between the flow velocity u _θ and the vorticity ω _θ .

が成立するため、乱れ渦度ω～の自己相関関数は下記式(46-7)のように近似できる。

When calculating the contribution to surface fluid flow pressure fluctuation, the following relational expression between the spatial derivative and the time derivative;

Therefore, the autocorrelation function of the turbulence vorticity ω ~ can be approximated by the following equation (46-7).

が成立するため、乱れ渦度ω～の自己相関関数は下記式(46-8)のように近似できる。

On the other hand, when calculating the degree of contribution to surface sound pressure fluctuation, the following relational expression between the spatial derivative and the time derivative of the sound pressure moving at the speed of sound;

Therefore, the autocorrelation function of the turbulence vorticity ω ~ can be approximated by the following equation (46-8).

When the right side of the above equation (44) is rearranged using the above equations (46-1) to (46-8), the left side of the above equation (41) is finally expressed as the following equation (47). ..

The right side of the above equation (47) corresponds to a portion of the "part integrated for the angular frequency band of interest" on the right side of the above equation (40) that contributes to the surface sound pressure fluctuation. Therefore, by substituting the right side of the equation (47) into the corresponding part of the equation (40), the following equation (48) is obtained.

Multiplying the integrand on the right side of the above equation (48) by "the square of the density of the flow field ρ ² " and rewriting the evaluation point z2 to the general notation z, the APDS calculation defined in the following equation (49). The formula is obtained. In the present specification, the equation (49) derived in this way is referred to as “a flow field at the evaluation point z in the flow domain 42” with respect to “the surface sound pressure fluctuation pa _θ (x) at the observation point x of the rigid body 41”. It is defined as an index showing the degree of contribution of. The reason for multiplying by ρ ² is that p ^* = p / ρ was used in the process of deriving the APDS calculation formula.

The approximate expression shown in the following equation (50) holds between the surface sound pressure fluctuation pa _θ (x) and the APDS (x, z) at the observation point x (Equations (38) and (48). And equation (49)).

That is, the integral value of the "norm of the surface sound pressure fluctuation pa _θ (x) at the observation point x" in the angular frequency band of interest (in other words, the autocorrelation function of the surface sound pressure fluctuation pa _θ (x) at the observation point x). ) Can be approximated as "a value obtained by spatially integrating the APDS for the observation point x in the flow domain". Therefore, APDS functions with high accuracy as an index showing the contribution of the flow field at the evaluation point z to the surface sound pressure fluctuation pa _θ (x) at the observation point x. The above is the description of the derivation of the APDS calculation formula.

(Calculation of IDS)
From equations (49) and (50), it can be considered that APDS represents "sound pressure generated by the spatial flow (sound source) of the flow field at the evaluation point z and reaching the observation point x via spatial propagation". can. Therefore, the "unit vector in the sound pressure propagation direction generated by the spatial flow (sound source) of the flow field at the evaluation point z and reaching the observation point x via the spatial propagation" can be expressed by the following equation (51). ..

なお、

は、観測点ｘにおける剛体４１の表面の法線ベクトルである。 From equation (2), equation (50) and equation (51), the sound intensity Iin _n (that is, the angular frequency band of interest [θ] incident along the normal direction of the surface of the rigid body 41 at the observation point x The spectral average of the sound intensity of any observation point x at [ _l , θ _h ] can be expressed by the following equation (52).

note that,

Is the normal vector of the surface of the rigid body 41 at the observation point x.

Further, by substituting the APDS equation shown in the equation (49) into the above equation (52), the sound intensity Iin _n can be expressed as the following equation (53).

The integrand in the equation (53) represents "the contribution of the flow field at the evaluation point z to the sound intensity Iin _n incident along the normal direction of the surface of the rigid body 41 at the observation point x". This integrand is defined as an IDS (Intensity Density Source) as shown in the following equation (54). Hereinafter, the IDS may be referred to as a "first index".

(Calculation of sound power)
The sound power Pin can be calculated by surface-integrating the sound intensity I in _n on the surface of the rigid body 41 as _in the following equation (55).

The surface integral of the equation (55) is defined as APwDS (Acoustic Pressure Power Density Source) as in the following equation (56).

上記式（５７）より、ＡＰｗＤＳは、「剛体４１の表面に到達する音響パワーＰｉｎに対する評価点ｚにおける流れ場の寄与度」と考えることができる。以降、ＡＰｗＤＳは「第２指標」と称呼される場合がある。以上で説明した指標（ＩＤＳ及びＡＰｗＤＳ等）を用いることにより、音響パワーＰ_ｉｎと車両周囲の流れ場との関係から、車内音Ｐ_ｏｕｔと車両周囲の流れ場との関係を分析／解析することが可能になる。 Therefore, the equation (55) can be rewritten as the following equation (57).

From the above equation (57), APwDS can be considered as "the contribution of the flow field at the evaluation point z to the sound power Pin reaching the surface of the rigid body 41". Hereinafter, APwDS may be referred to as a "second index". By using the indicators (IDS, _APwDS , etc.) described above, the relationship between the sound inside the vehicle and the flow field around the vehicle can be analyzed / analyzed from the relationship between the sound power _Pin and the flow field around the vehicle. Will be possible.

<Specific operation of this implementation device>
The specific operation of this implementation device will be described. The CPU 14 (simply referred to as “CPU”) of the calculation unit 11 executes the “analysis routine” shown in FIG. 6 every time a predetermined time elapses.

At the start of this routine, the CPU performs data from the vehicle model 20 to be analyzed for wind noise, data from the flow domain 21 indicating the analysis range, and unsteady CFD (numerical fluid dynamics) from the ROM 16 and / or HDD 17. ) The data necessary for the simulation and the data of the formulas (calculation formulas such as APDS, IDS, Inn and _APwDS ) necessary for the analysis of the wind noise are read out, and these data are stored in the RAM 15. In this example, the surface of the left front side glass 22 of the vehicle model 20 is defined as the "analytical surface".

At a predetermined timing, the CPU starts the routine of FIG. 6 from step 600, performs the following processes of steps 605 to 650 in order, and then proceeds to step 695 to end this routine.

Step 605: The CPU determines the time history data u (z, t) of the flow velocity of the flow field and the time history data ω (z, t) of the vorticity for each spatial node z in the analysis range (flow domain 21). Calculate each over time. The position of the space node z in the flow domain 21 is such that the space node z does not exist on the surface of the vehicle model 20 (that is, the space node z is separated from the surface of the vehicle model 20). It is preset.

Step 610: The CPU averages the time history data u (z, t) of the flow velocity and the time history data ω (z, t) of the vorticity, and averages each space node z in the flow domain 21. The flow velocity U- (z) and the average vorticity Ω- (z) are calculated.

Step 615: The CPU processes the time history data u (z, t) of the flow velocity calculated in step 605 by fast Fourier transform (FFT), and autocorrelates the turbulence flow paths u to _θ (z) in the angular frequency band of interest. Calculate the function. This autocorrelation function is calculated for each spatial node z. For example, when 2 kHz is selected as the frequency band of interest, the autocorrelation function of the turbulence flow velocity u to _θ (z) is calculated for each spatial node z in the flow domain 21 within the range of 1420 Hz to 2840 Hz. The above processes from step 605 to step 615 correspond to "unsteady CFD calculation process".

Step 620: The CPU calculates the IDS for the observation point x at each evaluation point z in the flow domain 21 based on the APDS calculation formula (formula (49)) and the IDS calculation formula (formula (54)). This process is performed for all observation points x on the analysis surface. As described above, if the node x on the analysis surface is defined as _xi (i: 1 to m) and the spatial node z in the flow domain 21 is defined as zj ( _j : 1 to n), the CPU determines. N IDS (the number of evaluation points z) for the observation points x _k are calculated. Since the CPU performs this process for all observation points x _k , it calculates mn IDS in total.

Step 625: The CPU calculates the sound intensity _Iinn according to the following formula (58) based on the IDS calculated in step 620.

As described above, the "value obtained by spatially integrating the IDS for any observation point x in the flow domain 21" represents "sound intensity I in _n at the observation point x". Therefore, the CPU extracts n IDS (x _k , z _j ) for the observation point x _k , and adds the extracted IDS (x _k , z _j ) (that is, IDS (x _k , z _j ). ) Is spatially integrated in the flow domain 21) to calculate the sound intensity Iin _n at the observation point x _k . The CPU calculates m sound intensity I in _n (the number of observation points x).

Further, the CPU transmits a display command for displaying the calculated sound intensity _Iinn data on the display screen 19 as an image to the output unit 13. Upon receiving the display command, the output unit 13 displays the data as an image on the display screen 19. FIG. 7 is an example of a distribution map of sound intensity I in _n on the analysis surface (left front side glass 22) displayed as an image on the display screen 19 based on the display command. The frequency band of interest is set to 2 kHz. In the example of FIG. 7, the observation point having a larger sound intensity Iin _n is associated with darker color data. According to this display, the user can recognize "a position on the analysis surface where the sound intensity _Iinn is large". That is, the user can recognize to which position on the analysis surface the acoustic intensity Iin _n , which has a large degree of contribution to the sound inside the vehicle, is incident.

Step 630: The CPU calculates the sound power _Pin according to the equation (55). That is, the CPU calculates the sound power Pin by dividing the sound intensity Iin _n calculated _in step 625 by the surface integral on the analysis surface. Further, the CPU calculates APwDS from the relationship between the equation (56) and the equation (57). As described above, _APwDS is "the contribution of the flow field at the evaluation point zj to the sound power Pin reaching the vehicle surface". The CPU calculates _APwDS at each evaluation point zj in the flow domain 21.

Step 635: The CPU displays a screen for inputting a reference value of APwDS on the display screen 19. The user inputs a reference value of APwDS (hereinafter, referred to as "first reference value").

Step 640: The CPU displays a screen showing the isosurface distribution of APwDS on the display screen 19 based on the first reference value. FIG. 8 is an example of the isosurface distribution of APwDS image-displayed on the display screen 19 based on the first reference value. Of the evaluation points z _j , the points where the APwDS value is larger than the first reference value are displayed in dark gray. That is, the position of the flow field having a high contribution to the sound power Pin is displayed in dark gray. Therefore, the user can recognize which position of the spatial flow in the flow domain 21 greatly contributes to the sound power Pin.

The CPU may display a screen for inputting a plurality of reference values of APwDS on the display screen 19. In this configuration, it is assumed that the user has entered a first reference value and a second reference value that is greater than the first reference value. FIG. 9 is an example of the isosurface distribution of APwDS image-displayed on the display screen 19 based on the second reference value. In the image of FIG. 9, the size of the dark gray region is smaller than that of the image of FIG. Therefore, the user can identify the position of the spatial flow that contributes more to the sound power Pin.

Step 645: The CPU displays a screen for designating the parameters constituting the IDS and a screen for designating the evaluation cross section of the designated parameters on the display screen 19. In this example, the parameters that can be specified are the average flow velocity U−, the turbulence flow velocity u to _θ , and the average vorticity Ω−. It should be noted that other parameters constituting the IDS (for example, the vector r connecting the observation point and the evaluation point) may be specifiable. The user specifies the parameter to be focused on with reference to the sound intensity Iinn distribution displayed in step 625 and the _APwDS isosurface distribution displayed in step 640.

Further, the user specifies an evaluation section of the specified parameter. In this example, it is assumed that the user has specified a cross section by the broken line L in FIG.

Step 650: The CPU causes the display screen 19 to display the distribution map of the parameters specified in step 645. FIG. 11 shows a distribution map of the average flow velocity U− (z) around the left side mirror 23 in the evaluation cross section (see the broken line L in FIG. 10). Further, FIG. 12 shows a distribution diagram of turbulence flow velocities u to _θ (z) around the left side mirror 23 in the evaluation cross section (see the broken line L in FIG. 10). By referring to these distribution maps, the user can refer to the characteristics of the spatial flow that contribute to the sound inside the vehicle (that is, the average flow velocity U- (z), the turbulence flow velocity u to _θ (z), and the average vorticity Ω. -(Z)) can be specified and the design (position, shape, etc.) of the left side mirror 23 can be examined.

<Reliability of indicators (IDS and ADwDS)>
Next, the reliability of the first index (IDS) and the second index (ADwDS) described above will be described. The inventor prepared an actual vehicle having the same shape as the vehicle model 20 shown in FIG. Hereinafter, the actual vehicle will be referred to as a "first vehicle", and the vehicle model 20 corresponding to the first vehicle will be referred to as a "first vehicle model".

The inventor measured the sound inside the vehicle with respect to the first vehicle. Further, the inventor performed the above-mentioned analysis processing on the first vehicle model using the present implementation device. Then, the inventor examined the result of the analysis process and moved the position of the left side mirror of the first vehicle to the front side of the vehicle by 200 mm and attached it. The vehicle whose design has been changed in this way is referred to as a "second vehicle". Further, the inventor has prepared a vehicle model corresponding to the second vehicle. This vehicle model is referred to as a "second vehicle model".

The inventor measured the sound inside the second vehicle. The inventor confirmed that the sound inside the vehicle was reduced as compared with the first vehicle. In this way, by changing the design (position) of the left side mirror, it was possible to reduce the noise inside the vehicle. The specific effect of improving the sound inside the vehicle is shown in FIG. 14, which will be described later.

Further, the inventor performed the above-mentioned analysis processing on the second vehicle model using the present implementation device. FIG. 13A is a “distribution diagram of sound intensity I in _n on the analysis surface (left front side glass)” when the analysis process is executed for the first vehicle model. FIG. 13B is a “distribution diagram of sound intensity I in _n on the analysis surface (left front side glass)” when the analysis process is executed for the second vehicle model. As shown in FIGS. 13 (a) and 13 (b), the magnitude of the sound intensity _Iinn is reduced throughout the analysis surface by changing the design (position) of the left side mirror. In particular, in the second vehicle model, the region (black region) of the acoustic intensity _Iinn , which contributes greatly to the sound inside the vehicle, is smaller than that in the case of the first vehicle model.

FIG. 14 shows "difference in measured in-vehicle sound between the first vehicle and the second vehicle", "sound power calculated by analyzing the first vehicle model using the present implementation device, and the present implementation device. It is a graph showing "the difference from the acoustic power calculated by analyzing the second vehicle model using." As shown in the graph, the error in the calculation result of the improvement effect by the analysis processing using the present implementation device is smaller than the improvement effect of the in-vehicle sound in the actual measurement. Therefore, it can be seen that the indexes (IDS and ADwDS) described above are highly reliable indexes for analyzing the sound inside the vehicle. Therefore, the wind noise can be analyzed with higher accuracy.

Based on the above, according to the present implementation device, by using the above-mentioned indicators (IDS and ADwDS) to identify the position of the flow field that greatly contributes to the sound inside the vehicle, the sound inside the vehicle can be efficiently and reliably obtained. Can be reduced.

Specifically, in the present implementation device, the isosurface distribution of APwDS is displayed on the display screen 19. The user can specify the position of the spatial flow that contributes more to the sound power Pin by appropriately setting the reference value of APwDS.

Then, the user specifies parameters (average flow velocity U-, turbulence flow velocity u to _θ , and average vorticity Ω-) having a relatively large contribution to the APwDS value with reference to the isosurface distribution of APwDS. .. The user can easily grasp the parameters that cause the APwDS to increase, and can more efficiently examine and change the shape of the vehicle.

Although the analysis device of the embodiment has been described above, the present invention is not limited to the above embodiment, and various modifications can be made as long as the object of the present invention is not deviated.

For example, in the above embodiment, the vehicle model is used as the structure model to be analyzed, but the present invention is not limited to this, and for example, a structure model such as an aircraft or a ship may be used.

The information displayed on the display screen 19 in step 625 is not limited to the example of FIG. 7, and may be any information regarding the distribution of the magnitude of the sound intensity I in _n on the analysis surface. For example, the CPU may display the position (observation point x) of the analysis surface on the display screen 19 where the magnitude of the sound intensity Iin _n is equal to or greater than a predetermined value.

The information displayed on the display screen 19 in step 640 is not limited to the examples of FIGS. 8 and 9, and may be any information regarding the distribution of the size of APwDS within the flow domain 21. For example, the CPU may display an image color-coded according to the size of APwDS on the display screen 19.

10: Analysis device, 11: Calculation unit, 12: Input unit, 13: Output unit, 14: CPU, 15: RAM, 16: ROM, 17: Hard disk (HDD), 18: I / O interface, 19: Display screen , 20: Vehicle model, 21: Flow domain, 22: Left front side glass, 23: Left side mirror.

Claims (1)

It is an analysis device that analyzes the wind noise generated in a moving structure.
The unsteady CFD calculation process that moves the structure model that models the structure is executed, and the average flow velocity and average vorticity of the flow field in the predetermined region of the flow fields around the structure model at a predetermined time. Is calculated for each spatial node, which is a node in the predetermined region, and a value based on the amplitude of the turbulence flow velocity in the predetermined region is calculated in the angular frequency band of interest, which is the angular frequency band for which wind noise is analyzed. , The first calculation means calculated for each spatial node,
Based on the average flow velocity calculated by the first calculation means, the average vorticity, and the value based on the amplitude of the turbulence flow velocity, along the normal direction at the observation point of the analysis surface in the structure. A second calculation means for calculating a first index indicating the contribution of the flow field at the spatial node to the incident acoustic intensity.
Based on the first index calculated by the second calculation means, the sound power reaching the analysis surface is calculated, and the contribution of the flow field at the space node to the sound power reaching the analysis surface is calculated. A third calculation means for calculating the second index shown, and
A display means for displaying information regarding the distribution of the size of the second index in the predetermined region, and
An analyzer equipped with.

Images