A prosthetic device is provided for treatment of an aortic valve, having a compressed state for transarterial delivery and being expandable to an expanded state for implantation. The device includes an expandable support implantable in the expanded state of the prosthetic device in an aortic annulus, and an inner envelope having an upstream portion that lines the inner surface of the support, and a downstream portion which, when the prosthetic device is in the expanded state, extends into an aorta and defines a diverging conical section having a diameter that gradually increases from an upstream end of the section to a downstream end of the section. The section is configured to produce, during systole, a non-turbulent blood flow into the aorta with pressure recovery at the downstream end of the section. Other embodiments are also described.