The native applications of both are entirely different, .apk for android coded in Java and .tpk for Tizen coded in C++. So its impossible to directly instal .apk files in Tizen.
But OpenMobile has created an application named ACL for Tizen which will run almost any android applications in Tizen platform.
First you will have to install the application in the Tizen device and you have to load the apk within the ACL application.
More info check their Datasheet