Does pi mining consume energy

the answer is no.

 How can Pi be mined on mobile phones without the energy consumption typically associated with crypto mining? 

Pi achieves this by using a different type of consensus algorithm on its blockchain instead of the well-known and energy-consuming Proof of Work (PoW) . Pi's consensus algorithm is based on the Stellar Consensus Protocol (SCP) and an algorithm called the Federated Byzantine Agreement (FBA), all of which do not require exhaustive energy consumption to reach consensus to secure a ledger. These types of consensus algorithms require nodes to form quorums and exchange messages with each other based on a confidence graph composed of individual quorum slices to come to a "consensus" on what the next block should look like. 

Mining is the process of contributing to a blockchain's consensus algorithm to secure its ledgers in exchange for rewards. While PoW mining requires high energy consumption for the nodes that "work" to solve mathematical puzzles that help the algorithm reach consensus, Pi mining requires a distributed confidence graph. The security circuits of each individual mobile miner are aggregated into a global trust graph that feeds the Pi blockchain consensus algorithm. Therefore, each mobile miner mines Pi by contributing to the intersectionality, security, and feasibility of the Pi blockchain's consensus algorithm to secure the Pi ledger. While PoW miners' contribution to these blockchains is energy, mobile Pi miners' contribution to the Pi blockchain is their trust relationships and the active affirmation of those relationships. The heavy work of running the consensus algorithm based on this confidence graph aggregated by the mobile miners is still done by the computing nodes. In fact, the Pi testnet already has more than 10,000 such computer nodes, which means that Pi is well on the way to creating a very decentralized mainnet.