Skip to main content
SpringerLink
Log in

Numerical Optimization of the Defrosting Performance of the Vehicle Based on Discrete Adjoint Approach

  • Published:
International Journal of Automotive Technology Aims and scope Submit manuscript

Abstract

In this study, the discrete adjoint approach with the grid deformation technique based on radial basis function was presented to solve the tough problem that the complex shape of the defrosting duct is very difficult to be optimized with multiple parameters in the improvement of the defrosting performance of vehicle. Firstly, the defrosting performance of a light truck was analyzed. Then the discrete adjoint approach was applied by taking the average Nusselt-number as the objective function. The normal surface sensitivity was used in the deformation of the defrosting duct. After 10 optimization cycles, the optimal model was acquired. The results show that, after optimization, the sum of the average Nusselt-number is increased from 3164.16 to 3350.54, which has a positive effect on improving the convection and heat transfer capacity on the windshield effectively. Compared with the initial model, the airflow of the outlet near the windshield is increased from 95.07 g/s to 96.94 g/s, the defrosting time required by the optimal model is reduced by more than 20s. Therefore, the discrete adjoint approach can optimize the complex shape of defrosting duct with multiple parameters effectively, which provides an effective method in the study of automobile defrosting performance.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

M :

objective function

W :

vector of state variables

X :

vector of grid nodes

D :

design variables

R :

vector of flow residual

Λ:

adjoint matrix

s(x):

deformation amount

X j :

position of control points

c j :

constant

δ :

constant vector

n :

number of control points

β j :

expansion coefficient

Nu A :

average Nusselt-number on the zone A

Nu a′ :

average Nusselt-number on the zone A′

Nu B :

average Nusselt-number on the zone B

A a :

average air velocity in the zone A

A′a :

average air velocity in the zone A′

B a :

average air velocity in the zone B

F :

F distribution

r :

pearson correlation coefficient

α :

significant level

φ j :

radial basis function of Euclidean distance between control ny grid node

References

  • Albring, T. A., Sagebaum, M. and Gauger, N. R. (2015). Development of a consistent discrete adjoint solver in an evolving aerodynamic design framework. 16th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conf. Dallas, TX, YSA.

  • Du, X., Yang, Z., Zhou, H., Li, Q. and Jin, Z. (2016). Numerical investigation of geometry effects on flow, heat transfer and defrosting characteristics of a simplified automobile windshield with a single row of impinging jets. SAE Technical Paper No. 2016-01-0208.

  • Gao, Y., Wu, Y. and Xia, J. (2017). Automatic differentiation based discrete adjoint method for aerodynamic design optimization on unstructured meshes. Chinese J. Aeronautics 30,2, 611–627.

    Article  Google Scholar 

  • Germanou, L. A., Papoutsis-Kiachagias, E. M., Delacroix, A. and Giannakoglou, K. C. (2016). Defroster nozzle shape optimization using the continuous adjoint method. European Cong. Computational Methods in Applied Sciences and Engineering (ECCOMAS Cong. 2016). Crete Island, Greece.

  • Goldasteh, I., Chang, S. I., Maaita, S. and Mathur, G. (2015). Numerical simulation of airflow distribution on the automobile windshield in defrost mode. SAE Technical Paper No. 2015-01-0330.

  • He, P., Mader, C. A., Martins, J. R. and Maki, K. J. (2018). An aerodynamic design optimization framework using a discrete adjoint approach with OPENFOAM. Computers and Fluids, 168, 285–303.

    Article  MathSciNet  Google Scholar 

  • Jahani, K. and Beigmoradi, S. (2014). Utilizing CFD approach for preeminent assessment of defroster air flow distribution and predicting windscreen deicing behavior. SAE Technical Paper No. 2014-01-0688.

  • Javed, S., Javed, F. and Samsher. (2017). Effect of boat tail profile on drag coefficient of a sedan using CFD. ASME 2017 Int. Mechanical Engineering Cong. Exposition (IMECE 2017). Tampa, FL, USA.

  • Kader, M. F., Youn, Y. M., Jun, Y. D. and Lee, K. B. (2009). Characterization of the HVAC performance with defroster grillers and instrument panel registers. Int. J. Automotive Technology 10,3, 305–312.

    Article  Google Scholar 

  • Kedward, L., Allen, C. B. and Rendall, T. C. (2017). Efficient and exact mesh deformation using multiscale RBF interpolation. J. Computational Physics, 345, 732–751.

    Article  MathSciNet  Google Scholar 

  • Kenway, G. K. W., Mader, C. A., He, P. and Martins, J. R. R. A. (2019). Effective adjoint approaches for computational fluid dynamics. Progress in Aerospace Sciences, 110, 100542.

    Article  Google Scholar 

  • Kumar, C., Makana, M., Regin, F., Garg, A. and Pedamallu, D. P. (2019). Windshield defrosting analysis: A numerical and experimental approach. SAE Technical Paper No. 2019-28-0115.

  • Kumar, V., Tare, K. and Kapoor, S. (2010). Deployment of CFD for optimization of the air flow distribution over the windscreen and prediction of defrost performance. SAE Technical Paper No. 2010-01-1059.

  • Nadarajah, S. and Jameson, A. (2000). A comparison of the continuous and discrete adjoint approach to automatic aerodynamic optimization. 38th Aerospace Sciences Meeting and Exhibit. Reno, NV, USA.

  • Patidar, A. (2010). Comparison of CFD Analysis Methods for Simulating De-Icing Pattern over Automotive Windshield and Windows. SAE Technical Paper No. 2010-01-0555.

  • Roy, S., Nasr, K., Patel, P. and Abdulnour, B. (2002). An experimental and numerical study of heat transfer off an inclined surface subject to an impinging airflow. Int. J. Heat and Mass Transfer 45,8, 1615–1629.

    Article  Google Scholar 

  • Saad, Y. and Schultz, M. H. (1986). GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Scientific and Statistical Computing 7,3, 856–869.

    Article  MathSciNet  Google Scholar 

  • Zhou, B., Albring, T. A., Gauger, N. R., Ilario, C., Economon, T. D. and Alonso, J. J. (2017). Reduction of airframe noise components using a discrete adjoint approach. 18th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conf. Denver, CO, USA.

Download references

Acknowledgement

The work was supported by the Science and Technology Research and Development Program of Chongqing Municipality (cstc2019jscx-fxydX0013).

Author information

Authors and Affiliations

  1. School of Automotive Engineering, Chongqing University, Chongqing, 400044, China

    Sishi Cao, Zhifei Zhang, Yunwei Huang, Quanzhou Zhang & Zhongming Xu

Authors
  1. Sishi Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhifei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yunwei Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Quanzhou Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zhongming Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhifei Zhang.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cao, S., Zhang, Z., Huang, Y. et al. Numerical Optimization of the Defrosting Performance of the Vehicle Based on Discrete Adjoint Approach. Int.J Automot. Technol. 22, 109–118 (2021). https://doi.org/10.1007/s12239-021-0012-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12239-021-0012-8

Key Words

Search

Navigation