Study On The Parabolic Equation Method For Predicting The Insertion Loss Of Sound Barriers

Sound barriers can effectively reduce the impact of traffic noise and industrial noise on the environment.In the practical process of using sound barrier to control environmental noise,it would be very beneficial to designing the geometry,the position to be mounted,and the structure of sound barriers,if the insertion loss of sound barriers can be accurately predicted in prior.The frequently used methods for predicting the insertion loss include the analytical method,the approximate method and the boundary element method(BEM).These three kinds of method can only be applied in the homogeneous environment where the sound speed and ground surface impedance are constant.However,in practical situations,these environmental parameters are varied with the position,i.e.the environment is inhomogeneous.For example,the sound speed will increase with the increase of height in the downwind case.Ignoring the variations of sound speed or ground surface impedance will make the insertion loss predicted by the above three kinds of method inaccurate.The parabolic equation method has the advantage of taking the inhomogeneity into account,and thus can be applied to the more practical outdoor environment.Salomons first used the Crank-Nicholson parabolic equation(CNPE)method to predict the insertion loss of sound barriers in inhomogeneous environments.However,the CNPE method developed by Salomons leads to large prediction errors when the sound source and the sound barrier is close to each other,and also costs too much time due to the large number of grid points when the receiver and the sound barrier is far to each other.These two drawbacks restrict the application of the CNPE method.The two drawbacks are studied in this dissertation,aiming at establishing a parabolic equation method for predicting the insertion loss of sound barriers which is free from the two drawbacks.The advances in the research of insertion loss prediction methods are first reviewed in this dissertation.And then the analytical methods for calculating the sound field of a point source above an impedance plane are presented for cases with and without the sound barrier.The results of the analytical methods can be used as a reference to examine the parabolic equation method.Next,the theory of CNPE is introduced,and it is found through theoretical analysis that the large prediction errors of the CNPE method when the sound source and the sound barrier is close to each other is caused by the Gaussian starting field which is valid only for sound waves with small elevation angles(e.g.,less than 10 degree).To eliminate the restriction due to the starting field,the Gaussian starting field is re-derived and high order starting fields that are valid for large elevation angles are obtained.Numerical simulations are carried out to compare the performance of starting field of different order.The results show that the Gaussian starting field of 4th order is the most appropriate one for the CNPE method,and the CNPE method coupling with this starting field is able to predict the insertion loss accurately even if the sound source and the sound barrier is close to each other.Finally,to solve the problem of the CNPE that the computational efficiency is low when the receiver and the sound barrier is far to each other,the insertion loss prediction method based on the Green’s function parabolic equation(GFPE)is proposed in this dissertation.The feasibility of the GFPE based prediction method is verified via numerical simulation.And comparisons of the calculation time consumed by the CNPE and the GFPE method demonstrates that the GFPE method can improve the computational efficiency significantly,especially at high frequencies.