Predicting unavailable parameters from existing velocity fields of turbulent flows using a GAN-based model

In this study, an efficient deep-learning model is developed to predict unavailable parameters, e.g., streamwise velocity, temperature, and pressure from available velocity components. This model, termed mapping generative adversarial network (M-GAN), consists of a label information generator (LIG) and an enhanced super-resolution generative adversarial network. LIG can generate label information helping the model to predict different parameters. The GAN-based model receives the label information from LIG and existing velocity data to generate the unavailable parameters. Two-dimensional (2D) Rayleigh-Bénard flow and turbulent channel flow are used to evaluate the performance of M-GAN. First, M-GAN is trained and evaluated by two-dimensional direct numerical simulation (DNS) data of a Rayleigh-Bénard flow. From the results, it can be shown that M-GAN can predict temperature distribution from the two-dimensional velocities. Furthermore, DNS data of turbulent channel flow at two different friction Reynolds numbers ${\text{Re}}_{\tau }=180$ and 550 are applied simultaneously to train the M-GAN and examine its predicting ability for the pressure fields and the streamwise velocity from the other two velocity components. The instantaneous and statistical results of the predicted data agree well with the DNS data, even for the flow at ${\text{Re}}_{\tau }=395$, indicating that M-GAN can be trained to learn the mapping function of the unknown fields with good interpolation capability.

Figure 1

Architecture of M-GAN: (a) generator and (b) discriminator, where LIG is the label information generator, CPP is the convolution-pooling part, RRDBs is the residual dense blocks, MSP is the multiscale part, and CBL is the convolutional-batch normalization-LReLU integrated layers.

Figure 2

Architecture of the AE-FE.

Figure 3

Schematic of the 2D Rayleigh-Bénard flow case.

Figure 4

Schematic of the channel flow case.

Figure 5

Predicted instantaneous temperature field of the 2D Rayleigh-Bénard flow case.

Figure 6

Statistical results of the 2D Rayleigh-Bénard flow case: (a) average temperature profile; (b) probability density function of temperature field.

Figure 7

Predicted instantaneous streamwise velocity and pressure fields of the turbulent channel flow at ${\text{Re}}_{\tau }=180$.

Figure 8

Predicted instantaneous streamwise velocity and pressure fields of the turbulent channel flow at ${\text{Re}}_{\tau }=550$.

Figure 9

Root-mean-square profiles of streamwise velocity and pressure fluctuations: (a) and (c) are $u_{\text{rms}}^{+}$ and $p_{\text{rms}}^{+}$ of the channel flow at ${\text{Re}}_{\tau }=180$; (b) and (d) are $u_{\text{rms}}^{+}$ and $p_{\text{rms}}^{+}$ of the channel flow at ${\text{Re}}_{\tau }=550$.

Figure 10

Probability density functions of the streamwise velocity and pressure fields of channel flows: (a) and (c) are $\mathrm{PDF}(u$) and $\mathrm{PDF}(p$) of the channel flow at ${\text{Re}}_{\tau }=180$; (b) and (d) are $\mathrm{PDF}(u$) and $\mathrm{PDF}(p$) of the channel flow at ${\text{Re}}_{\tau }=550$. The isoline levels are in the range of 10%–90% of the maximum PDF with an increment of 20%.

Figure 11

Spanwise energy spectra of the predicted streamwise velocity and pressure from channel flow at ${\text{Re}}_{\tau }=180$.

Figure 12

Spanwise energy spectra of the predicted streamwise velocity and pressure from channel flow at ${\text{Re}}_{\tau }=550$.

Figure 13

Predicted instantaneous streamwise (a) velocity and (b) pressure fields of the turbulent channel flow at ${\text{Re}}_{\tau }=395$.

Figure 14

Root-mean-square profile of the streamwise (a) velocity and (b) pressure fluctuations of the turbulent channel flow at ${\text{Re}}_{\tau }=395$.

Figure 15

Relative error of all the testing results, where case 1 is Rayleigh-Bénard flow and cases 2–4 are channel flow at ${\text{Re}}_{\tau }=180$, 395, and 550, respectively.