WinReal3D software for modeling of acoustic systems

Version 2.2

 

Alexander Yu. Sokolov

D.Sc,

Email to: [email protected]

 

Download program:

http://members.fortunecity.com/winreal3d/winreal3d.rar

 

 

 

  1. Introduction

 

Working in physics field and having made a lot of numerical simulations of shock waves, gas-dynamical and  plasma flows I decided to use this knowledge for speaker modeling. Indeed, the propagation of sound is governed by well-known equations.  Constantly growing power of modern PC was always attracting me to the problem of speaker analysis.

 

What You find here is my attempt to represent approach based on 3D wave simulations to speaker analysis. Several years ago I became an enthusiast of  DIY-audio (and tubes) and decided to start this project.

 

This program is completely free, my idea is to have feedback from users and same audio enthusiasts as me, this will also motivate my future ideas. I understand this approach is quite complicated, there are  some simplifications and restrictions (i.e. wall reflections), so more people and more ideas the better.  Send me You questions, suggestions, the speaker enclosures You want to see included into my program.

           

This tool allows for modeling of various speaker enclosures taking into account the location in room as well as reflections on the walls. Dimensions of room and speaker are linked to numerical grid (pixels). Next figure demonstrates main dimensions, i.e. room may have dimensions 5 õ 4 õ 2.6 m which in pixels becomes X1 x X2 x X3 = 125 x 80 x 52, one pixel equals 5 cm. The position of the speaker inside room is also set, i.e. r=1 m, e=1 m, microphone is placed  at distance  l=1 m in front of driver.

 

Fig. Position of the speaker and measuring microphone in the room 

 

  1. Calculation model

 

The model is based on finite difference method for numerical integration of differential 3D wave equation, taking into account the boundary conditions on the speaker surfaces and room walls (as well as ceiling and floor).

 

The driver model uses TS-parameters, the calculation is carried out based on Newton equation of motion. Particular pressure values on both sides of the diffuser are accounted for calculation of diffuser acceleration. The source amplifier can have finite (nonzero) value of output resistance.

 

Next figures demonstrate typical  3D solutions of pressure distribution in the room.

 

 

 

Fig. Speaker of closed box type. The pressure distribution in the room, frequency 143 Hz.

 

 

Fig. Speaker of closed box type. The pressure distribution in the room, frequency 359 Hz.

 

 

 

Fig. Speaker of closed box type. The pressure distribution in the room, frequency 905 Hz.

 

 

  1. Various types of acoustic enclosures

 

At present the following enclosures are included into the tool:

 

-    ideal point source (this is useful for checking the model as well as analysis of room modes)

-         folded baffle with single driver

-         folded baffle with two drivers

-         closed (sealed) box

-         rear opened box

-         sealed sphere

-         transmission line

-          transmission line 2 (folded)

-         Voight pipe

-         Onken

-         Bass reflex

-         TQWP

-         Back loaded horn (BLH)

 

Note: for Onken, bass reflex and BLH the inner channels (ports) must be wider than the grid size, at least two pixels are necessary to represent the channel width. Thus, it is recommended to reduce the grid as much as possible for these enclosures.

 

  1. Presentation of results

 

There are the following features of the software:

 

-         Simulation with given frequency. This is useful for visual analysis and better understanding of  acoustic wave propagation in the room;

-         Scanning of all frequencies. In this mode the frequency is gradually increased from minimum to maximum value, and the pressure level is determined at the measuring point. Such calculation takes much time as it is necessary to run each frequency for several hundred of milliseconds;

-         Fourier spectral analysis.

 

Fourier analysis is the most convenient and allows for calculation of amplitude and phase response at once. It is recommended to set integration (measuring) time of about 500 milliseconds or more for Fourier analysis. 

 

 

  1. How to start

-         Run WinReal3D

-         In menu “Action” use “Open Project” and select file “demo_project”.

Now the demo project is loaded and one can calculate frequency response.

 

These are several notes about the program:

 

All parameter are given in menu “Parameters” which includes:

1 “Driver” is used for driver parameters setting. “Calculate” helps to translate TS parameters into mass, compliance etc.
1.2 “Room” is used to set the room geometry and speaker and microphone position. All dimensions are given in pixels. By default 1 pixel = 5 cm. Grid size can be changed in “Grid size” menu.
1.3 “Speaker” is used for selecting from various types of enclosures. Mark “use this enclosure” to activate the selected type. The project file stores all enclosures such that they can be considered and compared to each other  during one session of work.
1.4 “Input” is used to set input voltage, amplifier resistance and the type of the signal: pure sine wave or pink noise (central frequency with side harmonics). It is advised to selected the sine wave.

 

Remark: The pink noise can be used only in “Sim one frequency” or “Scan frequencies”

 

1.5 “Duration” is used for setting of measuring time. Microphone has to be switch on after the first wave arrives to the microphone from the speaker, thus is it convenient to set this time as a distance (i.e. distance to the speaker) divided by sonic velocity Vs. The second time (switch off) is determined also as a typical distance divide by Vs. It is advised to select the measuring time (difference between mic on and  mic off) of the value of 500 millisec or more.

 

1.6 “Reflection on Walls” is used for setting the reflection coefficients on walls, floor and ceiling.

 

Remark: If the room is rotated (see “Rotate room”) only K=1 is applied on side walls.


1.7 Rotate room – see below.

To start simulation there are three actions in menu “Action”: 


1. “Sim one frequency” is used to start calculation with given frequency. This shows the structure and propagation of waves in the room. The values below the output window provide SPL for this frequency which was set in “Input” menu. If “wave packet” was selected SPL regards to this. 


2. “Scan Frequencies”: this option automatically starts the scanning of all frequencies, that is low frequency is calculated  at first, then the frequency is increased and so on. At the end SPL plot is shown. Each frequency is calculated for the measuring time determined in “Input”. This option requires considerable amount of time.


3. “Fourier” option is for Fourier analysis. IT IS RECOMMENDED TO START WITH THIS OPTION. Fourier includes calculation of one, two frequencies or white noise. Select “white noise” for calculation of amplitude and phase response. For Fourier analysis set the measuring time of about 500 millisec ore even more, see below.

  1. Accuracy of Fourier Analysis

 

To understand the accuracy of Fourier analysis let us set all reflection coefficients  to zero (K=0). This arrives us to the model of “no-echo” camera. In the model the walls are acoustically transparent which is done via the corresponding boundary conditions on the room surfaces. It is difficult to completely eliminate the reflections in numerical model, however, the reflecting waves are relatively small as it is seen from the examples below.    

 

 

Sine wave from ideal point source in “no-echo” camera.

 

The next figures shows the spectrums of ideal point source in “no-echo” camera in the range of 20-1000 Hz. The higher measuring time the better accuracy. Especially low frequency range requires sufficient averaging time as the period of wave is large.

 

6.1 Measuring time 300 ms

 

 

Spectrum of original signal 50 Hz

 

Spectrum of original signal 300 Hz

Spectrum of while noise

 

6.2 Measuring time 600 ms.

 

 

Spectrum of original signal 50 Hz

 

 

Spectrum of original signal 600 Hz

 

 

Spectrum of white noise

 

6.3 Measuring time 1200 ms (1.2 s).

 

 

Spectrum of original signal 50 Hz

 

 

 

Spectrum of original signal 300 Hz

 

 

Spectrum of white noise

 

Thus, for measuring times of the order of 0.5 sec or more the reasonable accuracy is achieved. At middle frequencies there is a small gain (+ 2dB). In principle this peak can be taken into account as the correction parameter for real speaker calculation (similar to  correction curve of real measuring microphone).

 

7        Some examples: Closed (sealed) box

 

 

Fig. Set initially  box dimensions as W õ H õ D=0.6 õ 1 õ 0.3 m (the wider side panel forward), V=160 liters. The driver is placed at 0.6 m from floor. Set reflection coefficients K=0, that is no-echo camera. The driver is 12 inch JBL123-A, the amplifier has R=2.5 ohm.

 

 

SPL in no-echo camera, measuring time 0.6 s.

 

Next we add reflections from the floor only (K=1). The other room surfaces are acoustically transparent. As it is seen SPL is increased by 3dB in low range (which is in theoretical agreement), however, the middle range is dropped (And one may think that is would be wise to play with soft carpet in from of the speaker to obtain the middle curve of two plots!)

 

 

 

SPL with reflection from the floor only. t=0.6 s..

 

Next, let us run the similar simulation but with all reflection surfaces having K=0.8. The SPL curve remains same “eye-pleasant”.

 

 

 

SPL with all room surfaces having K=0.8, t=0.6 s.

 

For the sake if interest let us rotate the speaker such that the narrow side of the box is in the front (narrow side toward the mic). At first we look at the SPL in “no-echo” camera:

 

 

Too lack of bass we have!

 

SPL for same volume of closed box but the narrow side is in the front, t=0.6 s, no-echo camera.

 

Switching on the reflection from the floor (K=1):

 

Same but with the reflection form the floor K=1, t=0.6 s.

 

Finally switch on all reflections from walls, floor and ceiling (Ê=0.8):

 

SPL of front narrow side speaker, K=0.8, t= 0.6 s

 

9. Rotation of speaker with respect to the room

 

This tool allows to place the speaker with the driver directed towards the center of the room, which is commonly used in reality. See the fig. below:

 

 

 

The angle of rotation is set in menu  “Rotate Room”.

 

Remark. When this option is used only full reflections on side walls (K=1) is used in the current version.

 

Remark 2. Calculation of room with rotations is slower than simple straight room.

 

Open project demo_rotated  for modeling of room with rotation.

 

10. Effect of internal box waves

 

This tool allows for accounting of the effect of internal box modes. Next figures show the calculated amplitude and phase responses under two conditions: (left) taking into account the effect of pressure at the internal surface on driver diaphragm motion and (right) neglecting by this effect. In the second case it is assumed that pressure disturbances near the diaphragm are zero inside the box. The speaker has dimensions of 1 x 0.5 x 0.3 m, such that the own box frequencies (half wavelength equals distance between walls)  are  170 Hz, 340 Hz and 570 Hz.  The integral behavior of the speaker exhibits two peaks at 170 and 340 Hz, and the third resonance is negligible.

 

 

       

 

 

11. Concluding remarks

 

As I already mentioned at the beginning this is an open project. One person cannot compare numerical model with all enclosures. If You find this program useful, write to me, if You suggest any improvements other users will also appreciate this.