Energy analysis of 2D electro-thermo-hydrodynamic turbulent convection

Abstract

Turbulent convection is ubiquitous in fluid systems. In particular, multi-physical convection problems involve mass, heat, and particle transfer. When the particles are charged and driven by a high-voltage electric field, both buoyancy and electric forces contribute to driving and maintaining the convection. In this work, we perform numerical analysis using a high-fidelity Fourier-Chebyshev spectral solver. We further derive the dynamical systems governing the kinetic energy, the enstrophy, the potential energy, and the electric energy analytically. Using the simulated data, we apply a long short-term memory recurrent neural network to predict the chaotic time series of domain-average energy terms. Finally, we perform a data-driven modal decomposition to show the coherent structures that contain energy and enstrophy in 2D turbulent convection.

Figures (6)

• Figure 1: The DNS snapshots and their 2D wavelet approximations at the second level ($A_2$) of $E_u$, $E_p$, $E_e$, and $\Omega$ for Case 8.
• Figure 2: The domain-averaged DNS energy and enstrophy and their 2D wavelet approximations at the second level of $E_u$, $E_p$, $E_e$, and $\Omega$ for Case 8. The domain-averaged values vary in time, $t$.
• Figure 3: (a) The training and validation loss $\mathcal{L}$ for Case 8 with $\Delta_\text{forward}=\Delta$, $\Delta_\text{back}=10\Delta_\text{forward}$, $n_{neuron} = 256$, and batch size $=32$; (b) the minimum validation loss ($min(\mathcal{L})$) with respect to $\Delta_\text{forward}$ and $\Delta_\text{back}=m\Delta_\text{forward}$ with $n_{neuron} = 512$, and batch size $=16$; (c) $min(\mathcal{L})$ with respect to $\Delta_\text{forward}$ and $n_{neuron} = [128, 256, 512, 1024]$ with $\Delta_\text{back}=5\Delta_\text{forward}$ and bath size $=16$; and (d) $min(\mathcal{L})$ with respect to $\Delta_\text{forward}$ and batch size $= [16, 32, 64, 128]$ with $\Delta_\text{back}=5\Delta_\text{forward}$ and $n_{neuron}=512$.
• Figure 4: Prediction of the normalized time series $\langle E_u\rangle_V$, $\langle E_p\rangle_V$, and $\langle E_e\rangle_V$.The LSTM has $\Delta_\text{forward} = 10\Delta$, $\Delta_\text{back} = 10\Delta_\text{forward}$, $n_{neuron}=512$, and batch size $=32$.
• Figure 5: The first 4 POD modes of $E_u$, $E_p$, $E_e$, and $\Omega$ for Case 8.