Preheat oven to 350 degrees F. Stir together the dry ingredients and spices.
Using a blender or food processor, blend together the sugar, apple juice concentrate, and eggs until well mixed.
In a small microwaveable bowl, microwave the water and ground flaxseed together for 30 seconds. Gradually beat the flaxseed mixture into the egg mixture along with the vanilla and the 1/4 cup of pineapple liquid.
Stir in the dry ingredients and then fold in the crushed pineapple, shredded carrots, and raisins. Spoon the mixture into an 8-inch baking pan sprayed with non-stick cooking spray. Bake for 20 to 25 minutes. Allow the cake to cool slightly before glazing.
To prepare the glaze, mix the apple juice concentrate and water until the concentrate is melted. Spread evenly over the cake.