In accordance with at least one aspect of this disclosure, a turbomachine cooling system includes a first low pressure port disposed in a low pressure portion of a turbomachine and a first high pressure port disposed in a high pressure portion of the turbomachine and in selective fluid communication with the first low pressure port via a cooling channel. The high pressure portion of the turbomachine is configured for a higher compression than the low pressure portion of the turbomachine where the first low pressure port is disposed. The cooling system can include a heat exchanger system disposed in the cooling channel such that a flow traveling from the first high pressure port to the first low pressure port is cooled by the heat exchanger system before traveling through the first low pressure port into the low pressure portion of the turbomachine.