Computational Fluid Dynamics (CFD) simulations are widely used for designing and optimizing systems involving fluid flow. However, these simulations are often computationally expensive, which restricts the scope of design space exploration and limits their use in many-query problems. Surrogate models based on Machine Learning (ML) have been proposed as a computationally efficient alternative to accelerate CFD simulations. These surrogate models can be trained using supervised data-driven and/or physics-informed learning methods. However, despite recent advancements, these training methods still suffer from the high cost of data acquisition and the computational complexity of repeated high-order derivative calculations. In this paper, we focus on using Physics-Informed Neural Networks (PINNs) to build CFD surrogate models and developing a novel method to improve training efficiency. The proposed method leverages knowledge distillation to mitigate the need for extensive training data, and to improve the prediction accuracy, as well as training convergence. It is particularly effective for making predictions over multiple unseen domains, significantly reducing the cost of training new surrogate models. We evaluated it on various computational domains with test geometries unobserved during training. The results show that even with limited CFD simulations used for training the teacher network, the proposed method accelerates the training convergence and prediction accuracy of PINN models compared to the vanilla training method.