Kafka Streams thread number
If I have 2 input topics, one have 10 partitions and the other have 5 partitions
Sounds good. So you have 15 total partitions. Let's assume you have a simple processor topology, without joins and aggregations, so that all 15 partitions are just being statelessly transformed.
Then, each of the 15 input partitions will map to a single a Kafka Streams "task". If you have 1 thread, input from these 15 tasks will be processed by that 1 thread. If you have 15 threads, each task will have a dedicated thread to handle its input. So you can run 1 application with 15 threads or 15 applications with 1 thread and it's logically similar: you process 15 tasks in 15 threads. The only difference is that 15 applications with 1 thread allows you to spread your load over across JVMs.
Likewise, if you start 15 instances of the application, each instance with 1 thread, then each application will be assigned 1 task, and each 1 thread in each application will handle its given 1 task.
what is the maximum thread number I can have in this case? 10 or 15?
You can set your maximum thread count to anything. If your thread count across all tasks exceeds the total number of tasks, then some of the threads will remain idle.
I recommend reading https://docs.confluent.io/current/streams/architecture.html#parallelism-model, if you haven't yet. Also, study the logs your application produces when it starts up. Each thread logs the tasks it gets assigned, like this:
[2018-01-04 16:45:26,859] INFO (org.apache.kafka.streams.processor.internals.StreamThread:351) stream-thread [entities-eb9c0a9b-ecad-48c1-b4e8-715dcf2afef3-StreamThread-3] partition assignment took 110 ms.
current active tasks: [0_0, 0_2, 1_2, 2_2, 3_2, 4_2, 5_2, 6_2, 7_2, 8_2, 9_2, 10_2, 11_2, 12_2, 13_2, 14_2]
current standby tasks: []
previous active tasks: []
Dmitry's answer does not seems to be completely correct.
Then, each of the 15 input partitions will map to a single a Kafka Streams "task"
Not in general. It depends on the "structure" of your topology. It could also be only 10 tasks.
Otherwise, excellent answer from Dmitry!