Former senator and Gov. George Allen and wife Susan greeted voters Tuesday morning at Washington Mill Elementary School, a precinct near their home in Mount Vernon.

Allen stopped to chat with Patch: “Well, our goal obviously is to win and the bigger the turnout the better," he said. "I think most people recognize that the larger the turnout the stronger it’ll be for us. We have a lot of support through Virginia because people know me.

"I had the honor of serving Virginians in the U.S. Senate, as well as governor, and I know the communities and the people, and that’s not something that’s easily done just in a year of campaigning," Allen said. "We have good friendships and relationships throughout Virginia, so the bigger the turnout, the better it’ll be for us. We’re cautiously optimistic.”

Allen faces competition in today's Republican primary for the U.S. Senate from three challengers: tea party member Jamie Radtke, minister E.W. Jackson and state Del. Bob Marshall of Prince William County. 

The Allens voted at their precinct and plan to visit other precincts around Northern Virginia today before heading to a rally in Richmond tonight to await results of the primary.

The winner will face Democrat Tim Kaine, also a former governor of Virginia. The Senate seat is currently occupied by Sen. Jim Webb, who announced his retirement last year from the Senate.

In a sampling of local precincts, not many voters showed up at the polls as of 2 p.m. today, except for the Hayfield precinct. 

Here's a breakdown of voter turnout percentages for four local precincts: 

• Hayfield: 7.8
• Rose Hill: 3.9
• Kingstowne: 2.5
• Franconia: Not yet reported 

Editor's Note: Lisa K. Brown contributed to this report.